Since FNV gave much more validity to melee/unarmed characters, I choose this option on my first playthrough. Dispite some great perks and useful weapons, there are a lot of situations where close combat seems to be the better option. The indoor areas, caves, vaults and various other buildings are quite tight, the player can easily find himself within arms reach of his enemies. Or in our case, the other way around. And even outside, ranged critters don't matter, the real heavyweights are the cazadores and deathclaws and when they get close I usually find myself a lot more comfortable with a good axe in hand ready to knock them down, succesfully disableing them, than fighting with some clumsy slow pistol or rifle that takes many shots to get the job done.
Thankfully close combat turned out to be very effective even on Hard or Very Hard difficulties and with the right abilities, you can make a character that is a true survival and a real beast even on it's own (though we plan on capitalize on our followers). What I like in melee/unarmed fighting is the simplicity of it, that it's always there as an option. They can take away your guns, but your fists are always with you and you can be a potent force even while being practically naked out there.
This guide will show you how.

Well without further abode, here's how the stats should be:

base / final
S - 6 - 9 (implant + Reinforced Spine)
P - 5 - 6 (implant)
E - 8 - 9 (implant)
C - 5 - 6 (implant)
In - 3 - 4 (implant)
A - 7 - 8 (implant)
L - 6 - 8 (implant + LR perk)

Strength
Actually you only need 9 in this if you plan to use the Ballistic Fist, which I ended up not using too much. Sure it's great against heavy armored opponents, but I ended up favoring other weapons. The requirement for the melee weapon Oh, Baby is 8, but I never used that either since it's a two handed weapon that slows you down. Actually I mostly ended up using the ever aweome fully modded Katana, that have quite low requirements but is not just really powerful, but fast as hell. And looks really awesome, even while sheated. Of course a high score in the brawn department does have it's uses, needless to tell.

Perception
Six points is the least and the most that is needed here solely for the Better Criticals perk. It's a must. Nuff said.

Endurance
Now HP is always welcome. Even though we don't deplete our pool of hit points too much, the more, the better, not to mention the bonus it grants for some skills me make use of. And we do need at least 8 for the wondorous perk that is Implant GRX.

Charisma
It's so common to make this stat as low as possible, but abusing power is not something any player with a healthy mind would do. To properly enjoy your game you need to like your character enough and that means you don't curse him with hideous looks. Not to mention that we plan take an excellent perk later called Ferocious Loyalty that has a Charisma requirement of 6.

Intelligence
4 in this wil lbe more than enough to get the necessary skill points and still being able to raise it to 10 with consumables (not like it's needed too much) We start out with 3, then the first thing we do before reaching level 2 is heading north to Sloan, then Near Black Mountain (you can use a Stealth Boy if you want though it is manageable without it), all the way to Durable Dunn's caravan wreckage for those Combat Armors that are left behind. After selling those to the Crimson Caravan and the Gun Runners, buy the Intelligence Implant for 3000 caps.

Agility
With 8 points, I never had any problem with my AP in VATS as it regenerated fast and I got plenty. Although I have to say, I fight in real time mostly and only entered VATS to perform certain special moves with some a melee weapons if needed or when fighting cazadors. Though you need 8 points in Agility to get the awesome Tunnel Runner perk which I find especially useful and fitting to this character.

Luck
After you got your intelligence enchanced, your second implant should be on this one. Then you're all set to win big at the Atomic Wrangler's Black Jack table for even more implants. Now the main reason to get this at 8 is of course the bonus it grants for critical chance and 8 is enough, I even had the comfort of not wearing the Lucky Shades (even through I got it for stealing some dogtags from NCR soldiers) just because I don't like the look of it. Same goes for the First Recon Berret, though with all these, you can raise your luck to 10 now if you want.


On to the Traits:

Hot Blooded
Fighting hand to hand or with a blade, my combat prowess is not affected by either Perception or Agility, but I've got tons of HP and the 15% extra damage is welcome. Get this as there are no other traits that benefits the close combat players too much anyway. Heavy handed is actually harmful as it only gives a pitiful bonus (what is a few points to a 15 percent increase?) and it reduces your valued chance for a critical hit.

Logan's Loophole
I know what you think, but believe me, this is the best thing ever. It actually gives chems a meaning, validetes their use, so you don't end up having 758546358236 psychos in your inventory at the end of the game out of fear of getting addicted to it. This trait allows you to be really powerful in combat since you can now spam tons of drugs and booze, which you'll find and craft. Literally, I was always high on several stuff without ever having to worry about getting addicted and with the combination of Chemist + Day Tripper, chems lasted for a hell of a looong time. This is not to be underestimated, my character basically lives in an other dimension thanks to this because instead of mere moments, Turbos are now lasting for friggin decades.
Now I feel that I have to clear some things here regarding the level cap this trait makes. If you fear that level 30 won't be enough for you especially with only 4 points in Intelligence and without the Educated perk, you're wrong. Trust me on this one. I do colllected all the relevant skill books and maxed out Melee, Unarmed and Sneak, and still can reach a 100 with Lockpick, Science and Speech with the help of equipment and consumables. So do I need any more? For Energy Weapons or what? I don't need any more skill points then what I can have at level 30 and with this, I aimed to bring out the most of my character, because the constant an harm-free usage of drugs and the booze + making them last for decades elevates us to a height which is unreachable for a level 50 character. They already maxed out their combat skills just as we did. The only difference between a level 30 and a level 50 character is that they have somewhat more base HP and had to dump more points to useless skills. Do you need to be proficent in another mean of defense form even though you already have the best possible, or have an ability that enchances your combat prowess even further without it's drawbacks? The choice is yours.
Guess you might swith to Wild Wasteland and learn the use of Explosives while getting some perks to back that up, just for the fun of it. But for me, I wanted to bring the most out of the chem-use in this game thus making my abilities even more powerful instead of having more, but neither as advanced.

Now for the Perks:
As I said, one of our main quality to focus is speed and we can be the fastest wearing Light Armor so we won't be slowed down. The first two perks resebles this approach as wearing Light, grants some other bonuses as well.
Make sure to invest enough skill points on the way to be able to take the next perk that is planned. One thing I should mention is that i's a good idea to hunt down as many skill books as possible. For example you MUST get one of the Dean's Electronics from Sloan for you to get your first perk at level 2 with the Intelligence implant already taken and Repair tagged. Yup, it's time for me to mention, make sure to tag Repair and Survival. For an easier route I guess you can cheat and take the Skilled trait first, then switch it to one of the two mentioned earlier just for the +5 points to every skill which might come handy. This is yours to decide. Anyway:

Light Touch
Travel Light - (It does make a difference and it even feels more than the 10% displayed)
Ferocious Loyalty - (Goes extremely well with Hot Blooded and the great companion nerve)
Stonewall
Super Slam
Silent Running - (Remember, speed is key and running should be always on from this point)
Purifier - (Lovely perk, so useful)
Piercing Strike - (Easily a must)
Better Criticals
Finesse
Ninja - (There is a mod for this to work properly, make sure to use it)
Chemist - (Make sure to hund down as much medical skill books as possible before reaching level 24! We don't want to waste too many skill points on this)
Slayer - (With Greased Lightning, the Katana or the War Club your attack speed will be insane)
Tunnel Runner - (With this and the OWB implant + T. Light, I sneak faster than most char run.)
Implant GRX - (Wonderful perk lasting a long time with this build. It will be available in Dead Money too. I also downloaded a mod that made it to be hotkeyed)

I wanted to include Unstoppable Force to the list, but we can leave that out as there are no more space to it. It's not important as the only guys who use to block my attacks ocasionally are the Legion and they are not such a big deal. Only fought them at the end of the game anyway. Not to mention that if you use VATS then they can't block your hits. Finesse is more useful overall.
It's a good idea to gather some achievement perks too relatively early. Tough Guy and especially Day Tripper will be great to have and of course the attack speed and damage increasing perks you get after a certain amount of battles come handy too.

Not much to say here, I went with Cass as a companion. She's just the most fun to have around. And have to say quite awesome in the Desert Ranger Combat Armor armed with the Riot Shotgun. Her Whiskey Rose perk gives me the bonus in DT + stats and my perks allowed me to be drunk for almost a whole day with just one bottle. Under these conditions and the fact that there are booze all around the Mojave, literally everywhere, it was not hard to remain wasted all the time. She's got two great combat perks and became really powerful even fighting on her own with the high companion nerve (it does make a difference) coming from the now alcohol enchanced Charisma of 8 (ocasionally I used some Mentats too to reach up to 10) and downright unstoppable when my HP went below 50% and Ferocious Loyalty kicked in.
She's not just pretty and witty but she's the perfect companion for this build. Great combat skills that goes well with our combat approach, while her way of drinking suits our consuming behavior.

Other than this, I went with ED-E, though Rex is awesome too. Upgraded this floating eye-guy with the Brotherhood to further increase the potential of the DR bonus of Ferocious Loyalty. Of course Rey can also recieve a DT increase with the brain of Lupa.

So that's it I guess. This character moves and attacks really fast and is powerful even on Very Hard. Gets by as he is but becomes a real beast when he pops in some hotkeyed drugs like Slashers and/or Turbos which you should craft a lot by the way since you can find and buy tons of Jet. Well, to be honest, Implant GRX or Turbo makes even the Courier's Mile a breeze for this melee/unarmed specialist (especially when using them with Rushing Water).

Hope this guide was revealing to some or at least provided a good read on the subject.