This is a guide for crewskills and crafting specifically as a free-to-play player(f2p). Information on this topic i found a bit scarce so i decided to write about it. Hope some other people that dive into the game find it usefull.

The information i found was usally a "don't bother" or "pick slicing" for a f2p player. After playing a while myself i do think you can engage with the crew skills as a f2p and have fun. Add to that that it is a decent way to get "stuff to sell at the GTN" aka make credits.

So to get the most basic questions out of the way:

Yes you can make credits with crafting/crew skills even as a f2p player.

As with most things involving credits it requires you to dive into the depth of the Galactic Trade Network and try your luck.

abbreviations used:
f2p= free-to-play(er)
GTN=galactic trade network (=auction house)

PS: english is not my mother language, so be so please be so kind to ignore the mistakes ;)

crafting storage

All your crafting ressources go in a storage shared between characters of a server. While ressources are in there all characters from the server can acess them, this enables you to craft primarily as a f2p. The amount you can put in there is unlimited (at least i have not found an upper limit).

You can manually acess that storage by opening the inventory (i) and then clicking the diamond symbol at the top. With drag left click you can put ressources from your characters inventory into that or just right clicking while the shared resource storage window is open moves them there.

Clicking ressources in your shared storage tab moves the whole stack into your characters inventory. Shift + left click to split stacks for example to sell a specific amount. Ressources in a character inventory are not counted for the shared ressource storage and only recognized for the character you are on.

The "basic" crafting supplies you can put in there, meaning ressource you gather or intermediate products. The end products you craft can not be put into that storage space and you still have to store them normaly, meaning via your legacy storage as a f2p.

crew skills

The way crew and the skills work is that you have 3 broad groups of crew skills that your companions can do. The skill is set by your character, so all of the companions from a character have the same crew skill.

Gathering skills are for picking up ressources in the field. Or you can send crews on mission with this where they bring back these gathering ressources. Missions meaning the crew does things and you do not need to walk around in the field to get ressources, it happens somewhat passive. Sending crew on missions costs credits and takes time. You can only send 3 members as f2p. You can not have the crew member as an active companion while he is on a mission. Crew missions give the companion influence and level your crew skill - no matter if the mission fails or not. Fails get you no ressources. Lucky crits give you more or special things. The ressources are automatically stored in the shared storage.

Missions skills as the name says only offer the mentioned crew missions. No gathering in the field. Missions skills get you ressources that are automatically stored in the ressource storage and depending on the skill some other items like companion gifts, crafting blueprints or item boxes.

Crafting skills just produce things. They do not level companion influcence. You craft intermediate products that can be stored in the ressource storage, but are put in your inventory after crafting, so you have to manually put them into the crafting storage. These Intermediate products count as crafting ressources by the game and therefor can be put in the shared crafting storage.
The final items you have to store like normal items, since they are just that - normal items. As f2p you can even craft level 60+ and artifact authorication things, which both you can not use, only sell.

All crew skills go up to level 600 by default. To unlock level 700 max you need to go to your trainer and pay 250k credits at level 600 for the unlock. Missions and ressources are seperated into grades, which is a sort of level indicator, but by no means corresponds to the rarity of the ressource.
Unlocking the 700 crew skill max gives you on gathering/missions skills more and higher grade 11 crew missions (you only have 2 grade 11 missions at crew level 600). For crafters it gives you the higher level shematics/blueprints. (Depending on what you want to do this might not be worth the credits.)

As f2p you can craft through the shared storage, even with the limit of 1 crew skill per character. Since each crafting skill requires 1 gathering and 1 mission skill to make things. So you need 3 skills, aka 3 characters. Or you could just buy ressources from the GTN (depending on the skill/items/ressources very pricy, i would not suggest this esp as f2p).

To level a crafting skill you need the corresponding gathering skill. Just to level crafting you do NOT need the mission skill. The leveling can be done by crafting intermediate products=components, that are then used together with the items from the mission crew skill to craft final items. So just for leveling a crafting skill you only would need 1 character with a gathering skill and 1 with the corresponding crafting skill, meaning 2 characters in total as f2p.

Each crafting skill needs some crew skill merchant items. These cost credits and are used to craft the intermediate products. You can store them in your shared ressource storage. If you have crew skill trainers the merchant that sells these items is close by. The items are mainly a credit sink and are consumed when you craft the intermediate products. They are fairly cheap you should be able to easily buy a stack of 100 or 200 of these each time. The later ones are a bit pricier, but you should have enough credits then to buy them.

For a crew skill overview and what needs what i suggest to just SearchEngineOfYourChoice for a chart there are a lot of them out there that show this quite good in the layout you want. (sth like: "swtor crew skill overview" will get you a bunch of pictures with a layout you like)

understanding slicing in the crew skill overview

Slicing is a bit of an odd skill and weird to understand if you are new to crafting. The best way to view it is as some sort of supplementary skill. It is not needed to craft the things the crafting skill does. But for a few special items and the rarer armors you need some slicing ressources.

For example an armor crafter (armormech) can still craft all armors without it. It would be rare armors with better stats that need slicing ressource to craft. Since the look of these armors is the same like the ones not needing slicing components and most of the time you use these armors in the outfiter anyway - where stats do not matter – slicing is not needed. The similar is true for the other crafting skills.

The other things that need slicing ressources on the crafters are Fabricator Crytals. These need Archeology too, so you might not even have one of the needed skills depending on your choosen crafting skills. These Fabricator Crytals are intermediate products needed to craft items called universal prefabs, which you can trade against decorations for your stronghold with some traders. The universal prefabs itself need input from 2 different crafters, which you do not have as f2p. So the final item is offlimits anyway. Stronghold decorations are just deco and you can get some otherwise, unless you absolutly want a specific item only obtainable through the prefab traders, this item and therefor slicing is not needed.

If you absolutly need slicing ressource for something there is always the option to buy it via the GTN or use your fourth character to learn slicing to cover the skill or drop a crew skill to learn slicing for a short while.

Overall if you want to craft as f2p is up to you. If you don't craft, i at least suggest to pick up a gathering/mission skill on all your characters to sell ressources and get a bit companion influence this way. If you do not care at all about crew missions and selling things pick slicing.
No matter what you do crafting takes time and i suggest to get companion influence to at least 20 before starting. You can do that pretty easy+cheap and it speeds things up considerable. I would suggest doing that for your gathering/misson crew skill characters too. The higher the companion influence the better of course, especially for crafting.

In terms of credits crafting takes a bit of time to break even, since you have to buy the initial blueprints from the trainer and some crafting ressources (+ maybe run of few mission skills to get blueprints you want or buy from the GTN). You do not make millions fast, but you can make a good profit if you set your mind to it. I personally did synthweaving and found it fun to do and i do sell the final armors/robes usally, not intermediate products and do get a few credits from that.

The main problem with crafting for f2p is the final products are most of the time not worth 1 million credits. You have 2 auction slots per character as f2p so you can sell for example 2 armors for a few hundred thousand credits maybe, depending on the armor/robe this differes, but usally prices are way under 1 million credits per piece, a potential profit most of the time under 1 million for both. Your other option for your auction slots is to sell a resource/component stack worth excatly 1 million on each auction slot, a potential profit a 2 million credits (actually 2x 920k after the auction fee, but besides the point here). To this comes selling the ressources from crafting might get you more credits then the final armor/robe/item you crafted overall. In Terms of profit selling ressources/components might seem better, but you might have a better shot of selling the cheaper final crafted item a few times then a stack of ressources/component once. If you get the ressources to craft yourself the initial credit worth of the ressources might not matter much, at least it does not to me.
To that comes the auctions slot limit as f2p. The final product takes only 1 auction slot. If you try to sell the intermediate product or ressource from the final item you would need multiple auction house slots.

Another final consideration for crafting or crew skills in general: You are on fairly even footing with subscribers and prefered status players. Meaning you can craft the level 60+ and artifact authorization items and sell these. You can get crew skills to level 700 and companions to influence level 50 (yes a bit grindy, but doable as f2p). Only difference you can only send 3 crew members on missions or to craft, the other players can deploy more at the same time. But other then the last restriction crew skills are very even for f2p compared to prefered/subscrbed players. It suffers the least amount of restrictions for the most part in my opinion.

In the end what direction you take here is up to you. If you craft final products, just components or not at all - your decision. Crafting is not a "quick way to make millions". In terms of credit return the approaches are quite even i would think, at least from my experience of selling some synthweaving robes or ressource stacks or intermediate products/components. They all depend on you handeling the GTN, really just the difference is what you sell.
Crafting/Crew skills are not in a good spot at the moment in general, but i find it fun to do nontheless.

in detail - why pick at least a mission/gathering skill if you do not craft?

The reason is math + credits :D

At crew skill level 600 the two grade 11 missions get you 220 companion influence each, the missions itself costing you ~5k each, at crew skill level 700 you get 280 influence with a mission cost of about 7k. You can quickly set these missions before you log off. Your companions will do them while you are offline. You get some ressources to potentially sell and companion influence this way.

The high level companion gifts cost you 10k, depending on the influence level of your companion you get different returns in terms of influence here, the higher the influence level of your companion the less you get (with all the perks ~600 influence at 20+, ~300 influence at influence 40+). The crew mission influence return stays the same regardless of your companion influence level. Even if you sell the ressouce from the crew mission absolutly cheap this is worth it in terms of credit balance, especially later on higher companion influence. Your companions will not level fast with this, but it less time standing around giving gifts.

(random info: On slicing 700 at grade 11 the credit cost should be roughly even with the credit case. Meaning you would gain companion influence without losing much credits in theory, but companions do fail the missions some times too. So in practice you still lose credits with the credit cases and getting slicing parts and selling these will be the way to make more credits here.)

Pick the ones you like, maybe even for roleplay reason.

I am ust adding my thoughts here below if you want to min/max a it slightly. My recommendation is mainly based on what you get when you loot gathering nodes in the world and the crafting skills they lead into keeping in mind how usefull it might be as a f2p. For crafting i am taking into consideration if it will potentially sell stuff althrought what sells is dependend on the server and market, so please remember that. In the end i think they all come out fairly even.

(personal note: i have only done synthweaving, a bit of armormech and a bit of artifice together with the appropriate gathering+mission skills for these and slicing. For the other skills this is just my opnion + experience overall from playing the game so far.)

Bioanalysis
Gather nodes for ressources and if you kill beast type monsters this creates a node to loot. Or run crew missins for ressources.
This is a maybe, I personally never did this one, but killing enemys to create nodes is convient. My two reasons i suggest not chosing this:
1. the crafting resulting from this(Biochem) is not worth it for a f2p itself due to how scaling works, only to potentially sell things.
2. most of the heroics you do to farm do not have beast type monsters or killing them is a waste of time.
The resulting crafting skill Biochem makes consumable stuff, so the gathering skill might be a good skill to just sell ressouces fairly regularly. It depends in the end if the crafting connected with this sells items or not in my opinion. I do not know that, thats is why i wrote a maybe here.

Scavenging
Gather nodes for ressources and if you kill robot type monsters this creates a node to loot. Aka same as bioanalysis, but for robots. Or run crew missions for ressources.
A fairly good option to choose. It can give ressources for three crafting skills armstech, armormech and cybertech. Heroics you do regularly on both faction sides have robots you have to kill for the objectives.

Archeology
Gather nodes for ressources. Or run crew missions for ressources.
The best option possibly. This gives ressources for synthweaving and artifice, with artifice being the skill that makes dyes and dyes being consumables a decent sell+use. Some heroics have some nodes on the way or you can run rounds in an area collecting nodes, but mostlikely you will tend to do the missions to get ressources for this.

Slicing
Gather nodes for credit cases (= credits) or run crew missions for ressources or credit cases.
Worst gathering skill to choose, but best for low interaction with crew skills in general, since the nodes only give credits. This is suggested fairly often for f2p, but is by far the worst option to choose from currently from the gathering skill if you want to gather stuff (game version 7.0).
If you do not want to engage with the GTN/auctionhouse/crew skills at all this might be the best/only skill. The credit cases are in crew missions too, they break roughly even to the mission cost. If you do not care about crew missions/crafting and maybe just want the companion influence from the missions pick this.
The credit cases are nice, but on other gathering skills the ressources you get from nodes are usally worth more then the credits the credit cases slicing gets you. Getting a node in the field takes some seconds to loot and the rewards do not compare to other equivalents (credit worth of ressources you get from for example a scavenging node). If you just run crew missions you can avoid the credit case crew missions then slicing is fairly even to other gahtering skills. So it is still a decent option, but only if you disregard gathering node rewards, which is what gathering skills are about partially – at least in theory. All in all worst gathering skill if you want to take time to gather nodes.

Pick what fits here to your crafting skill or if you want to just sell ressource what sells best.

They are the same, all can run crew missions. All can get ressources, some companion gifts and they can get you some schematics for crafting. The companion gift missions you can avoid, the schematics are random drops from mission were your companion crits = just rng. Investigation can get you certain schematics for all crafting skills. The fitting mission skill for your crafting of choice will get you schematics for your crafting. The schematics are usally not worth much (few exceptions depending on prices as always), but you can try to sell them or use yourself. A certain grade of mission will only get you certain schematics as possible drops. So this is one of the reason to run lower grade crew missions.
There is no best skill here. The only two considerations would be what sells better or what crafting you want, depending on that pick the skill here.

Overall i think there is a bit of a hierachy and i explain why below. I think some are simply better then others as a choice for f2p specifily in terms of what you get from them. That being said i am sure you can make a profit from the other crafting skills if you try in case that is your concern here and my recommendation should by no means discourage you to pick what you want.

As f2p you should be on your second or third character by the time you pick a crafting skill, so at that point you probably have some rough idea yourself what is good/bad or what you need or what sells better for credits. Changing your mind at that point which crafting to pick is not a problem. Switching gathering/mission skills is quite easy and is something i would recommend if you think another crafting skill is better. You lose nothing when switching gathering/mission skills (only the level progress and maybe the 250k if you extended it to crew skill level 700, but the credits you can easily get at level 60). Switching crafting skill costs more for that reason i recommend to play a bit before choosing (and you loose the blueprints, so maybe you get some mission skill blueprints that would be lost if you switch crafting skills).

Most crafting skills can produce mods for your gear, but you do not need these at all as f2p. (i think biochem is the only exception here, the rest can make mods) The reason i never mention mods below as a reason to pick a crafting skill is as a f2p you do not need the better mods you can potentially get with crafting. The mods from the supply section on the fleet if you want to mod gear are fine or just use the heroic gear from the crates without mods.
To that comes the process of making good/better mods is cost+time intensive(deconstruction over and over to get better blueprints). For yourself you do not need these better mods, to sell the higher level ones are absolutly not worth since 7.0 removed mods for 75+ players and you can only craft 75 ones no level 80 ... so yeah overall the sad truth is that crafting mods is currently not worth the effort at all. No one needs the high level one. The only reason to do this would be for roleplay reasons.
Thats why i never mention mods below as a reason to choose a crafting profession. But the professions have their respective mods, like armstech gun barrel mods, artifice lightsaber hilts etc.

Biochem
Not needed as f2p. This is a buff food/consumable skill. With this skill you can use better buff consumables, it is the only skill that gives an advantge. Since most content is easily doable as f2p you do not need the buff consumables. With how scaling currently works in 7.0 (aka it is broken) i am not even sure these buffs will get you any benefit at all at the moment. The only instance i can think of the buff consumable would be nice is if you do group flashpoints(=short dungeons) with other players and you get scaled up to max level 80. But then then lack of skills as a f2p is a much bigger issue then a minor stat increase.
The skill itself is the only one that has a direct benefit so for most not-f2p people doing higher content i think the obvious choice. I would guess that on most main characters other people have this skill together with the appropriate gathering+mission skill. For these reasons i do not think this is worth it. But I never used this, so i might be wrong on the potential here.
(random info: med kits usally sell for a very low price[few hundred credits] compared to armor parts [few thousand credits] if the ressources from deconstruction of med kits sell well it might be worth for decent profit.)

Cybertech
No, worthless because this makes mostly mods, which are currently worthless high level and you do not need as f2p yourself. Can make Earpieces that gives stats, which you do not need as f2p. It makes ship parts for the space missions ... if you like these tunnel space shooter missions then this is a maybe.(but you could maybe buy these things via GTN/auctionshouse, it would be a one time investment).
The only thing that maybe justifies this in my opinion is that you can get blueprints to make your own speeders/mounts with this. Which is nice kinda, but you can only make 4 (Vectron Archaeologist/Bioanalyst/Scavenger/Slicer) and the game has tons of options to get different speeders from even as f2p. The blueprints for these vectron speeders you could get possibly on the GTN for cheap, but the ressource depend on the type and may require more/different crew skills then the usal combination. If you buy the needed ressources it might not be cheap or you have to switch crew skills on your non-crafter characters (or use jawa junk/scrab)
Overall i think as f2p this crafting skills brings barely anything or nothing to the table. Maybe in future patches this might be worth it, currently it is not.

Armstech
Maybe, mainly because with the weapons being included into the outfitter For that it might be worth for the weapon looks, but other then that i do not see it being a usefull crafting skill as f2p.
Currently you can only craft a few modable weapons, i think alone for that it is not woth it. The rest of the weapons you can craft has fixed stats, so only useable for looks. You can only craft weapons usable for the tech classes.
As a f2p there are a lot of places to get different looking modable weapons. With cartel market weapons being a thing most people use these, so there is not really a great market to sell either in my opinion. Thats why this is mostly a no, with a maybe if people want weapons crafted from this for the outfiter.

Armormech/Synthweaving
Decent choice. Both are similar, thats why i put these together. Just robes or armors depending on the skill. You create all pieces from a set if you have the blueprint/shematic. From the skill trainer you can get a bunch of blueprints. You can use the crafted armors/robes yourself or sell them. You have a few options to just craft a different armor/robe if one does not sell. Quite a few blueprints you can get from the mission skill. You can deconstruct armor/robes/adaptive gear that you get (depending on the cost of ressources not worth it).
Armors and robes can be used by all classes, most are adaptive anyway. (random info: A class with only light armor can use a heavy armor in the outfitter.)
The Downside is this falls a bit short on the selling point, since armors/robes are no consumables. And there are a lot of places you can get armors even as a f2p so a bit of competition, but some crafted armors/robes are unique/rarer. Crafted armors/robes look different on imperial and republic characters too. So i think this is solid, because multiple options to sell or use yourself to give your characters a different look.

Artifice
Overall the best choice as f2p in my eyes. Dyes are consumables. You can use them yourself or sell them. Using dyes increases your options to create different outfits for yourself. You can create two lightsaber crystals with these that you can use yourself as f2p (cartel market crystals are still better due to collections), other crystals you can potentially sell (they have artifact authorization aka not useable as f2p). Most reputation tracks can get you a dye shematics to use as an artifice. So if you intent to do them for a reputation armor/weapon/item you want there is something additional you can get out of that for your time and effort.
You can make some lightsabers with artifice depending on if you like these or they sell for looks might be a plus point (similar problem like Armstech, nearly all lightssabers are not modable, meaning only for the outfiter/looks). You can deconstruct off hand items, lightsabers and relics.
I think the versatility makes this the best overall choice of the crew skills. The downside is a lot of people sell dyes for the same reason. Depending on server and prices dyes might be cheap to buy, which might make this not as good of a choice to craft yourself and buying dyes might be easier.

700 vs 600 crew skill.
To get crew level 700 you have to get to your crew skill trainer and pay 250k credits. This amount might seem a lot at first, you can farm that amount fairly easy at level 60, but it might no be worth it. A few things you should consider here:
for 600
The highest level ressources might not be worth the most credits so you might not need the higher yield grade 11 missions if your goal is to sell ressources. The best selling final crafting product might not need grade 11 ressources, so crew missions you run regularly you can do without the crew skill rank up.
Lastly a bit of a minor thing to considers is that selecting lower grade crew mission if you are max skill takes more mouse clicks then dropping the skill and leveling it from scratch to get low grade ressources. You would loose out on efficieny/return of ressources here per mission, but is a consideration and worth knowing.
For 700
When logging of i tend to do the most time intensive crew mission, meaning the highest grade one. Getting higher grade 11 mission might be worth then in the long term to get more ressouces and companion influence. You can run 3 crew members, at 600 you only have 2 grade 11 missions with 220 influence, at 700 you get some with 280 companion influence.

Relearning/dropping/changing/switching crew skills
You can drop you current crew skill by opening the skill window (b-key) and clicking the small x next to the skill progression bar. If you do that you lose ALL progress and blueprints if you are a crafter. Your new skill starts at 1 again. You lose the 600 to 700 unlock. To pick up your new skill you have to go to the crew skill trainer of your new skill.
For gathering/mission skills you just have to level them again. Before doing that i would suggest checking if you have discovery missions open, since you lose them. For crafters i would not suggest to do this, since you lose unlocked blueprints too.
As f2p switching crew skills is something that is a viable option. Especially the gahtering skills are super easy to level up if you pick up some nodes in the field. You should not be afraid to do this even if you have unlocked the level 700. You can switch a character between gathering and mission skills for your crafting and get all crafting ressources on one character this way. You just have to stockpile the ressources a bit and plan a bit, but it is doable. This way you only need 2 characters, one to do one crafting skill and another get the ressources.

Lower level vs higher grade ressources
Ressource grade is not an indicator how rare something is. Lower grade ressource might even be easier to farm/gather and the crew missions are faster. The prices differ and it might be worth to get a bunch of lower grade ressources instead of getting higher ones. Even if the higher grade ressouce is worth a bit more it might still be worth to get the lower ones in terms of time/cost effectiveness.

deconstruction
Crafting skills can deconstruct things. Depending on the type of skill different items. As a general rule of thumb what a profession can craft it can deconstruct in terms of item types.

synthweaving deconstructs robes (most adaptive armor gear from heroics at level 60 i can deconstruct on my jedi)
armormech deconstructs armors (deconstruct armors, adaptive gear from heroics works here too)
artifice deconstructs lightsabers+relics+offhand stuff
armstech deconstructs weapons (stuff that makes bum aka all the tech weapons)
biochem deconstructs med kits+stims (i am guessing)

Deconstructing things gives you some ressources back. Depning on the items cost and ressource prices this might be worth it and is a decent way to get a bit more credits compared to just selling it to a random vendor. From what i can tell it is a bit random on how much you get back and varies slightly in the amount, but it is usally not much. You can get some of the crew skill merchant items too or some augment components(=another crafting item) too.
Deconstruction of certain items can get you new blueprints. If that is the case with the deconstruction window open the item has an added tool tip with sth like "30% chance to get a shematic". For example robes you crafted with your synthweaver and deconstruct you have a chance to get a blueprint. The blueprints are usally only "refined"/rarer blueprints of existing ones you crafted. Some can give you hidden equipment sets that look different (for armor+synth crafting). I don't think there is a complete list of all these sets/items you can only get through deconstruction, or at least i have not found one.
Deconstructing random drops or the gear from heroics can only get your ressources, no blueprints. The heroic crate items at level 60 as f2p get you grade 8 ressources/stuff.

jawa junk/scrap/droid parts
You get these on some crew missions sometimes. Some login rewards give these. Both sources are random. So far i have not found a reliable way to get these as f2p other then running crew missions and cross my fingers. (Max level 80 players get these just from deconstructing gear aka super easy.)
You can not store jawa stuff in your shared ressource storage, but it is legacy bound, so can be put into your legacy storage.
On the fleet cartel market section (take some elevator to get there or quick travel point) you have jawas that can trade these for any basic crafting ressource. Any means really any. Higher grade ressources cost more, but you can get any green/blue/purple ressouce your heart desires.
Unfortunatly as f2p you do not get much of these. Over time you might get a stack of few hundered jawa stuff, but as mentioned high grade ressources cost a lot more. It is usally just worth to get lower ressources or maybe you are one ressource short and want to get it this way.
It might be a way to get the occasional slicing ressource if you need it or some rare low tier ressource.
The ressouce indicator/return might have an influence on how much you can get on crew missions (the "rich, bountiful" ressource return indicator on the missions), but i am not sure that is just my impression/guess. If that is the case it might be a reason to get the 700 upgrade, since when logging off i usally just run the most time intensive crew mission (=highest grade i got).

what crew skill to pick on your first character
For your first character i suggest to just pick any gathering skill and pick some nodes while questing if you feel like it. The crew missons from the gathering skill i would not suggest running early on or while doing your quests. The mission completion pops up while in cutscenes aka destroys immersion. Add to that the mission cost a bit and stack up and you want your credits to use for other things most of the time (like leagacy perks or speeder training etc). You can get a few ressources from nodes if you have a gathering skill and want to sell via GTN early to get credits.

I think bioanalysis or scavenging are the better choices for a first character since killing enemys creates a node and you do not have to get out of your way to find nodes (the lazy approach). If you want different skills you can switch these later, so picking something to get any ressources is better then picking nothing here.

companion influence
The higher the influence the better. This holds true mainly for crafting, since crits can give you double components. You can craft and run crew missions even with low companion influence.
When gathering nodes the influence does not matter.

I suggest at least influence level 20 before starting crafting, since this is quite easy+cheap to reach.
Influcence level 1-15 ->tier 1 gifts, 15-20 ->tier 2 gifts, 1-20 cost about 150k credits this way
rest the 10k credit gifts. For a bit of a break down use SearchEngineOfYourChoice "swtor Companion Gift Efficiency Guide".