• Fight everything you meet. It's way easier to advance the crystarium later and it also reduces the need to farm in certain places in the game.
  
• Save the game everytime you can and always on a new save. It is easier to get back somewhere if you feel like you missed something. Also I advice spending crystarium right before saving the game.
  
• Everytime your team changes, also change the paradigms. It is a lot more convenient if you do fight the way you want. Not the way the game does.
  
• Use Libra or Librascope on new enemies, check their weaknesses and adjust the paradigms.
  
• Go in every corner of the map, because there are a lot of
  treasures hidden there. They also contain weapons, which are available to purchase, but for a lot of gil - we don't want that to happen. The map isn't that big, you can do it lazy ass.
  
• Don't sell any components nor weapons until Chapter 9 before Primarch boss battle. It's important to upgrade before the battle, because it is going to make it hella easier.

This is the place when you can touch the "shop" and "upgrade" functions of save point.
Earlier it isn't really needed, but if you know what you're doing you can try upgrading the weapons. It is a bit unnecessary tho, also you don't have most of the best balanced weapons right away, so it could be a bit hard to do so.

These are just a few tips which I didn't do when I was first passing the game, huge mistake.

There are a few places in which you can choose your team, when it's possible I usually go with Lightning, Fang and Hope/Vanille. Snow is also relevant, but I just prefer to use Fang. And choosing between Hope and Vanille is that just Hope is a synergist and Vanille is saboteur. If you choose Vanille here you will have two saboteurs.
The best paradigms are I think:

As stated before the team I'm going to describe here is Lightning, Fang and Hope/Vanille.
The most important attribute you want to go for these are:

• Physical damage for Lightning
  
• Health and physical/magic wall for Fang
  
• Magic and healing buffs for Hope/Vanille

The equipment is also split in two parts - pre-chapter 10 and early chapter 12.
I will create two sections in case you don't want spoilers. :)
Also don't worry about other characters - upgrading is universal, I'm just going to show it on the example of Lightning, Fang and Hope. I can expand it to the rest of characters if needed.

Here is the equipment I'm using for boss battle at the end of Chapter 9 probably till Chapter 12 to the point I find endgame weapons.

As you can see I still haven't upgraded Fang's weapon, there are two reasons for that - I needed to buy Hope's weapon, cause I sold it earlier (I made a mistake) and thus I had less gil for components. It isn't too bad tho, I'm using her mostly as Sentinel, so I'm not focusing so much on her.

Heck, I need to sell the useless accessories.

I will also mention Vanille's weapon, because she might be better than Hope. :p

In chapter 9 you fight a lot of PSICOM soldiers who drop Credit Chips and Incentive Chips. They give a lot of money, so once you reach the end of room screenshoted in the first section you can go to the save point > shop > select any shop > sell > components and sell all those chips.
A lot of gil, right?

You can also sell unneeded weapons and components (except catalysts ) if you don't have enough gil for all the things down below, but it shouldn't really be a problem.

Wait, you didn't buy anything yet, right? Read this first!

Every weapon needs components to upgrade. There are two types: Organic and Synthetic.

• Oragnic are for giving EXP multiplier. You need 36 to apply the highest (x3) multiplier. The best are Sturdy Bones, Vibrant Oozes and Barbed Tails which are all bought at the Creature Comforts for 80gil each.
  
• Synthetic are for actually upgrading weapons. Here we will be using Crankshafts bought at the Lenora's Garage for 840gil each, since more valuable components unlock in Chapter 11.

What you're gonna do is:

1. Buy 36 Sturdy Bones, Vibrant Oozes or Barbed Tails
   
2. Buy 99 Crankshafts
   
3. Go to upgrade
   
4. Choose the weapon - Blazefire Saber for Lightning (base weapon), Hawkeye for Hope (found in Gapra Whitewood or bought for 4 400gil at Up in Arms), Gae Bolg for Fang (found in Palumpolum or bought for 13 100gil at Plautus's Workshop). For Vanille it will be Pearlwing Staff (found in Lake Bresha) (I strongly disagree on buying weapons, because it's only a waste of gil)
   
5. First apply Sturdy Bones, Vibrant Oozes or Barbed Tails - 36 for a x3 multiplier.
   
6. Secondly choose Crankshafts, select needed* and upgrade. (It is really important to use the exact amount (or a bit bigger) not to lose the multiplier.)

*Blazefire Saber = 38, Gae Bolg = 108, Hawkeye = 51

Did it show a star?
Yay. You upgraded your weapon to current max level.
It's all you can do at this moment.
You can do the upgrades earlier of course or each weapon one after another, but remember to prioritize Lightning's weapon, because she deals the most damage.

So crafting here is bascially the same with the only difference being catalysts needed for further upgrades. The best component is Ultracompact Reactor from R&D Depot. They cost 50 000gil each and with a x3 multiplier they provide 120 000EXP. You can also use Particle Accelerators (10 000gil at R&D Depot, 14 400EXP with x3 multiplier), but they are far less effective. We're still going to need Sturdy Bones, Barbed Tails and Vibrant Oozes.

Let's talk about each character separately just to make things clear. I'll make a table with needed EXP (quantity of components and catalysts) under these short descriptions.

The best weapon for her till endgame is Blazefire Saber, because it has the best balance. Once you get to Chapter 12 you can switch to Lionheart found in Eden, which is a bit worse, but has the Quick Stagger ability, which is very useful.

Gae Bolg is the best if you use her as Sentinel (I highly recommend to do this). I hardly ever use her as any other role, so the best choice for endgame would be Taming Pole, which you can find in Oerba Village. It does have Stagger Lock, but it isn't so bad as far as you use her only as Sentinel or supportive Commando.

The first weapon of choice would be Hawkeye, which is mentioned before. When you finally get to Eden you can find there Otshirvani, which is going to be the best weapon since it has Siphon Boost. It makes some of Ravager's abilities stronger and since he's mostly used as Ravager it's going to fit well.

Here's the table with catalysts upgrades for early weapons.


Endgame weapons here, with same order, Lightning, Fang, Hope.

Additional one for Vanille:

Upgrading weapons can be grindy and exhausting, but it gives a huge buff. I strongly recommend to farm at least a bit, you will experience it on your own, even better if you upgrade weapon to max level in one go. Then it is the easiest to see the difference.

I repeat that I based this guide on one that I found in internet, just made it clearer and easier to reach (TL;DR + on Steam).

I hope you enjoy this guide, I will be greatful for feedback on this one, since it's my first. :)