One thing that really helps to get a hang of gurps is to look at other people's character sheets. Their is a lot of variety, and the Iconic ISWAT characters only brush the surface.
The Mook has
a page of ready made gurps characters. These are fairly basic, have side explanations of how different mechanics work, and don't have point numbers attached, but they can give you a good idea of what someone else's character looks like. there are a lot of resources on the page. Do a search on the page for "sniper" to get in the right area.
It might be helpful to the OP if people put example snipers they've built or seen used in games they've played here.
EDIT: I found an old west sharpshooter I played for a bit in the PbP forums. He's only 100 points though, and he's more of a scout and survival expert than a warrior.. which isn't entirely inappropriate for an ATE sniper. The majority of his points are in talents, perception, and the riffle skill, so he has very flat primary stats. He's also way under the power level You're looking for, but the list of skills may be instructive.
David Egan, age 32
Scout, Guide, Sharpshooter
Code:
ST 10 HP 10
DX 10 will 11
IQ 10 per 13
HT 11 FP 11
Speed 5.25
Move 6
accented Spainish
Broken Apache
Broken Navaho
Stalker Talent 3
Hard to kill 1
Signature Gear (gun)
Signature Gear (Demon)
Cannot Harm innocents
Vow (wanderlust)
Charitable (CR 15)
Guilt complex
Skinny
Religious (quirk)
Dislikes coyotes (quirk)
Survival (Desert) per A 14 4
Survival (Mountian) per A 12 1
Survival (plains) per A 12 1
Wrestling DX A 10 2
Guns (Riffle) DX E 15 16
Riding (Horse) DX A 11 4
Navigation (Lands) IQ A 12 1
Stealth DX A 13 2
Tracking per A 15 1
Camoflage IQ E 13 1
Observation per A 12 1
Animal Handling (Horse) IQ A 10 2
Animal Handling (Cattle) IQ A 10 2
Veteranary (Hoofed beasts) IQ H 9 2
Knot Tying IQ A 9 1
Scrounging per E 13 1
Area Knowledge (Four Corners) IQ E 12 4
Hiking HT A 10 1
Carpentry IQ A 9 1
First Aid IQ E 12 4
Immediate Action Guns(riffle) A 13 2