My basic tool list would go as follows:
Gunsmith's Screwdriver set - I'm still using the set I bought from Walmart years ago because it was cheap and likewise the bits were cheap and some broke, moral of this story is don't go cheap on the screwdriver set.
Precision Screwdriver Set - These are useful for adjusting trigger screws and other small jobs. I buy the cheap ones because I constantly loose one or two of the drivers.
Torque Wrench - When I started out I bought two Seekonk wrenches and associated bits, one for 65 in/lbs, one for 15 in/lbs. The Seekonk wrenches are a great product but limiting in terms of versatility. Spend the money on the Borka Tools Torque Wrench, I've been using mine for a couple years and love it, simple, light, and has multiple settings for common torque values when dealling with rifles.
Pin Punch Set - I've been using the same Lyman set for years now, it works and don't see any reason to "upgrade" except that I plan to get some roll pin punches soon.
Hammers - I have a dead blow hammer and never use it but I've found a little ball peen hammer to be really useful and for when I don't want to mar something I have a hammer than has a hard rubber head and a hard plastic head.
Vice - A good vice is essential. When I bought my vice I also bought a set of pads from Brownells that are made from aluminum with an elastomer surface that grips well and doesn't mar the surface finish, these are worth their weight in gold. Of course before that I simply used a couple pieces of masonite board from a drawer, not pretty but functional.
Allen and Torx Drivers - I think it's a good idea to get a set of folding allen and torx wrenches, they're just handy to have when you don't want to dig through the umpteen bits to find the one you need.
LED Light - Great for checking out the dark corners of a rifle or a drawer or a scary room...which ever.
It might also be a good idea to have some common adhesives and such like red and blue Loctite, some super glue, and JB Weld for the little things that come up. Out of all of the tools that I have on, in, and underneath my work bench those are probably the ones that get used the most. Well that's not true, I didn't list the Dremel tool...a home gunsmith's bestest buddy..however a word of caution...a Dremel can be your best friend on a project or a complete cash suck that causes you to have to buy things twice and work three times as hard. If you get one just remember slow and steady. Hope the list helps.