Alexander hit it right on the head about the 3 in 1 machines. I have one and it can be a real pain having to re-tool. It was all I could afford at the time (can't even afford it now) and is a cheap but stoutly made Harbor Freight machine. But it's ideal for making jags, finishing ramords, &c. and I have made lock parts and a complete lock with its help. But if you want to do any barrel work, you're restricted to pistol barrels or very small diameter rifle barrels. Also, most have a limited speed range and it's generally too fast. The dials on the cheaper machines are also in metric and excessive backlash is often a problem. I don't know what kind of capital you have to work with or the shop space planned, but I would invest in a good full sized lathe with at least 1-1/2" spindle opening and as many speed settings as possible. Also the capability to cut threads. If you plan on doing barrel work try to get a large enough lathe to be able to turn the entire length without re-setting the barrel to finish the cut. You can get tooling that will allow you to mill with a lathe. With either, the important thing is to get something built heavy enough to do whatever job you need to do without shaking and chattering.
Now, unless you plan on making all your parts and need the above as well as a forge and anvil (plus hand tools) and a casting set-up, all you really need is some good quality wood chisels, screwdrivers and files. A good drawknife can be handy to have. The most used tool I have for stock work is a four-in-hand file. For cutting a barrel channel a router is mighty handy if you don't want to chisel and scrape. By the way, some scrapers would be handy to have. A Dremel tool with variable speed is great to have but you really have to be careful with it. Sanding drums, diamond bits, various shaped cutters can all be used to get into very tight places such as in the lock mortise. But like I said, be very careful, one wrong move can ruin days of work. Stay in control of it and think ahead. Don't ask me how I know. And of course a hand drill and a drill press with numbered bits as well as the fractional ones. When you tap a hole, most of the time you'll use a number bit to drill. And lots of assorted grit sandpaper. Don't forget to light your work area as well as possible. You'd be surprised at what the little shadows hide. You may think that you are cutting on one side of a line until your piece is seen in a better light afterward and you find that you cut on the other side.
I know I've left out a lot, but I've rambled on enough this time around. Good luck!