there are many types of builds in fallout new Vegas from sniper to all round gunner to me lee and sneak.
sniper build 
for a sniper the most likely thing to do is to stay as far away from your enemy as possible so perception and sneak for the critical hits are vital

strength: 6 
perception:7   +4 eyes trait + pre-war hat = 10 
endurance: 6
charisma:1
inteliance : 6 
agility: 10 
luck: 4 -  get implants
 
for the starter perks choose 4eyes and small frame. 
when you get to upgrade stats try and make your guns and sneak 40, it should only take 1 level up.

perks 

lvl
2 - confirmed bachelor
4 - comprehension
6 - bloody mess or shot gun surgery ( shot guns should be used as back up in close quarters)
8 - commando 
10 - fitness
12 - sniper
14 - centre of mass (70 guns)
16 -  better critical
18 - tag!
20 - grim reapers spirit
22 -  action boy (you can get at level 16 but wait till now because the perks at lvl 22 arnt very well fitted for sniper build
24 - chose either bloody mess or shot gun surgery depending on which one you didn't get at lvl 6 
26 - nerves of steel
28 - doesnt really matter but i think intensive training



AMOURS - THE ARE A HUGE RANGE OF AMOUR IN FALLOUT NEW VEGAS FROM HEAVY TO LIGHT THE BEST FOR THIS BUILD WOULD BE LIGHT I RECOMMEND GLASSES, 1ST RE CON BERET  AND BOUNTY HUNTER DUSTER OR CHINESE STEALTH AMOUR.