Fallout: New Vegas is even older than Skyrim so why should I bother treading upon territory already trod by countless others? Well, my Skyrim builds really bring in the blog traffic and advertising revenue. All of you progressive suburban white kids are making it possible for me to eat out at Chick fil-A twice a month. And in many ways FONV is a superior game. So I may as well... give it a shot. Haaa.
The pros recommend taking Guns as your offensive skill if it's your first time in the Mojave Wasteland because it's damn near impossible to screw up a guns build. My first toon used energy weapons. It's a science-fiction RPG so I decided to embrace the science-fiction feel. To be sure, guns and ammo are plentiful and comparatively cheap. Energy weapons and cells are rarer and more expensive. Like Rose of Sharon Cassidy said, it will behoove you to become a crack shot with energy weapons in order to save on ammunition and weapon maintenance. And in gameplay terms, that means critical hits.
Energy weapons are stupidly powerful if you take perks which increase your crit chance. If you use VATS to consistently (and psychotically) score head shots, you will quickly become the Doctor Doom-like king of the Mojave. When choosing your initial SPECIAL stats, you want to jack up your Luck as high as possible. There's a significant increase in your crit chance and skill at the blackjack tables starting at a Luck of 7. It's not a bad idea for your Luck to end up as a perfect 10 after implants or Intense Training. Here's how my guy started out:
S - 4
P - 6
E - 6
C - 3
I - 7
A - 6
L - 8
Strength is at 4 because after one implant or the Weapon Handling perk you are able to wield the Gauss Rifle, the best energy weapon in the game. In retrospect, I probably didn't need to have Intelligence that high, but I felt it added to the role playing experience. Similarly, if you're a power gamer you can drop Charisma all the way to 1 if you like. The two skills it affects, Barter and Speech, can easily be raised through skill points alone.
If you've got all the DLC, then the level cap is raised to 50. I was able to max out all but a few skills, namely the other offensive skills like Melee and Unarmed. At the start you should tag Energy Weapons (no shit), Science, and either Speech or Repair. These are the perks I took:
Level 2: Intense Training (Luck)
Level 4: Educated
Level 6: Vigilant Recycler (it sounds boring but it can save you a fortune)
Level 8: Bloody Mess (more damage is always good)
Level 10: Finesse (more crit chance = must have)
Level 12: Math Wrath (I like VATS. Plasma Spaz is also a good choice.)
Level 14: Jury Rigging (An excellent choice for any build)
Level 16: Better Criticals (You're damn near unstoppable now)
Level 18: Plasma Spaz (or Math Wrath if you didn't take it earlier)
Level 20: Grim Reaper's Sprint (optional at this point, but again, I like VATS)
Level 22: Laser Commander
There aren't as many dedicated energy weapons perks as the other offensive skills. You can take Meltdown if you like, but I didn't care for it as I damaged myself and my companions just as much as the bad guys. Pretty much every other perk available is up to you. Personally, I think the best factions for my Doctor Doom/Lex Luthor like characters are either Mr. House or Wild Card. Democracy is a bunch of bullshit and Caesar's Legion is mired in ignorance and stupidity.
EDIT, 4/1/2014: As most people have guessed, this is definitely not an optimized min/max build. It was literally the first one I ever played, before I knew more about the game mechanics. This is my revised min/max no-fun-allowed version:
S 5, P 6, E 7, C 1, I 8, A 6, L 7. Tags: Energy Weapons, Science, Repair. Perks: pretty much the same except take Light Touch at level 2, and Strong Back at level 8. It's really hard to screw up a build in this game if you're playing on normal difficulty.