Cowboy? Herp derp.
Cowboy Repeater < La Longue Carabine < Trail Carbine < Brush Gun
LLC will be quite difficult to acquire. Trail Carbine is available earlier, although getting hold of a scope is a matter of luck.
Here's my Cowboy build:
ST 4 (With Weapons Handling, you can use the Brush Gun)
PE 6 (For Better Criticals; can keep it ar 5 if you can reach the New Vegas Medical Clinic by level 16)
EN 7 (For maximum S.P.E.C.I.A.L implants)
CH 4+ (Whatever's left after you invest into everything else, but don't drop it too low.).
IN 7-8
AG 5-6 (You need at least 5 for Rapid Reload; I like taking 6 for Silent Running).
LK 6 (For Better Criticals).
Traits: Fast Shot, Built to Destroy, Small Frame. Any two out of these three will do fine. Small Frame is always helpful with the S.P.E.C.I.A.L. choices, Fast Shot makes you shoot faster (the penalties are insiginficant if you stick with rifles over revolvers), and Built to Destroy is the only way to raise your Critical Hit chance with almost no downside; all cowboy guns are EXTREMELY durable (well, except Ranger Sequoia, which is super-brittle at only 80HP) and very cheap to repair with Jury Rigging.
Skills to tag: Tag Speech, Barter, Explosives at Goodsprings (Explosives for dialogue check with Easy Pete and for the dozen or so sticks of dynamite- most expensive thing you can get at the start to sell for nice caps). When leaving Goodsprings, respec to Speech, Lockpick and Science.
Perks, necessary:
Quick Draw
Rapid Reload (WIth cowboy guns, this one's a MUST)
Comprehension
Hand Loader
Cowboy
Finesse
Better Criticals
Jury Rigging
Weapons Handling
Perks, optional:
Educated
Pack Rat (Does wonders for weight management)
Strong Back (Still more weight management)
Silent Running
Confirmed Bachelor/Black Widow (Quite useful if you plan to be enemies with Caesar's Legion; they're all male).
Bloody Mess (Damage increase is very small, but if you can't think of a perk to fill that last slot...)
Scrounger (Might help you find more of that rare 45.70 ammo. No guarantees though).
Gear, if roleplaying:
Any cowboy or Sheriff's hat
Sheriff's Duster