Sounds like part of what you need are some good templates to use for springboarding off of. As you're doing something of a post-apocalypse (albeit I assume very close to the apocalypse itself), the
After the End series may be of use, particularly
book 1, which has the character templates.
GURPS Template Toolkit 1: Characters may also be of use, but as I don't own that one I can't say for certain (there's a very,
very high probability it's useful for figuring out how to design characters, however - Kromm tends to make good stuff).
If you're not looking to spend any more money just yet,
GURPS Skill Categories is a free download, and it groups skills in a much better way than the Basic Set's alphabetical list; I typically use it when designing characters from scratch.
If you don't have a point budget, you may want to just start building and see where you end up. Seeing as you're basing your character off of Fairbairn, you may get some use out of
GURPS Martial Arts: Fairbairn Close Combat Systems. Note the preview PDF has a character sheet for the man himself. Modern snipers tend to be a good deal larger than Fairbairn (indeed, most contemporary soldiers tended to be bulkier). Take a look at the
Generation Kill miniseries; the actor portraying Rudy Reyes (the sniper) is actually Rudy Reyes himself.