99% of smithing is all done with hand tools, files and stones are your friends. A surface plate and a few small jigs help a lot for filing and stoning surfaces to keep them true. SLOW and check often.
While I wouldn't stop anyone from running out and grabbing a surface plate (on sale at Lee Valley Tools for ~$40, pretty regularly) I wouldn't consider it a must have, either.
Most gunsmithing is hand tools and brains. If you can't handle working well with both working at once...maybe another hobby, eh?
Dremel Tools are a pretty good rig for some stuff, they can wreck stuff faster than hand tools too. That 'brains' thing again.
A good place to work, a decent bench vise, some bench blocks (hockey pucks are good places to start) a decent set of screwdrivers, some files (you don't need a set, as much as you need a bunch of different files that fit your needs, whatever they may be), some stones, a few measuring tools, and a couple decent reference books will go a long ways.
Once you get started, the sky is the limit, you can generalize, specialize, focus on woodwork, checkering, or assembling black plastic poodle shooters from parts, or make black powder guns from scratch. The tools you buy are going to have to be tailored to the jobs YOU are doing.
If you need a place to start, start by reading as much as you can and see what you may seem to need for what you are interested in. Be aware that a great many of the classic works, like Howe's Modern Gunsmithing, are full of a lot of useful information, but are written in a different time, so you will have to sort out the stuff that applies, from that that does not.
Hit a few used book stores and see what you can find in the way of old School texts from shop classes at various levels. Lots of the stuff you need to know USED to be taught to all grade school kids as part of the general curriculum, before the wisdom decided that getting ones hands dirty was for peons and that the future was all in University educations.
The "Annuals" from Popular Mechanics magazine contain a LOT of good info too.
Cheers
Trev