A combat skill of some kind - guns, melee, and so on. Speech is pretty handy, since you usually get more EXP and good karma for talking people out of things than for killing them. Sneak is very useful too, but that depends entirely on your play style. Repair, lockpick, medicine and so on are all useful but mostly for checks in conversation and crafting (or opening specific boxes), which means you should stop them at 80 and use a skill mag when needed. You don't want to do that for guns as much, since you'll need that all the time.
Depends on your play style. For me it's guns, just for overall killing power. Lockpick is good to, you can get all the goodies of the wastes. Also, some type of Close range style is good to fall back on if all else fails.