For Fallout 1, I usually do: Traits: Gifted + Finesse, Tag: Small Guns + Stealth + one other (usually barter). Stats: Get Perception, Agility, and Intelligence to 10, luck at least 6.
Then, boost Small Guns as much as you can while getting barter to 80-100. With that barter, you'll have unlimited cash. Now, the key part of this build, unlike the Fast Shot builds above, is that you ALWAYS use targeted shots. Focus on critical hits; get the More Criticals and Better Criticals perks ASAP. Aim for the Eyes. If your hit rate on the eyes isn't high enough, get more small guns. Also, sneak everywhere in combat situations; you often will only alert the creature you're shooting (even though silenced weapons don't exist...) if your sneak is good enough.
This is a bit different from my Fallout 2 build, usually Gifted + Fast shot, tag Small, Big, and Energy guns, run and gun like a beast using the heaviest weapon you can find (or a gauss rifle)