THE most used and most critical tools a gunsmith will need is the best gunsmith screwdriver set you can afford.
The industry standard are the Brownell's Magna-Tip driver bits with two "law enforcement" size driver handles.... one magnetic, and one clip-tip.
Good punches are a must and possibly the best are the Brownell's replaceable pin type.
Instead of having to order and wait for a new punch to arrive, you simply unscrew the end and insert a new pin.
You can buy three sizes of handles and buy a number of types of pins, including started punches, roll pin punches, and others.
For stones, today's standard are ceramic. Unlike natural or standard synthetic, ceramic don't dish out as they wear, and don't dull the sharp edges.
Buy the best quality files you can afford, start them out on brass, and after they start to dull, finish up on steel.
Probably the best file type is the "Flat Hand" file. These come in lengths from about 3 inches to over 12 inches.
These have parallel edges and sides, with no taper.
Buy a few files and as you discover you need them, buy more.
Store the files in some manner where they can't touch each other and dull.
Buy better quality Swiss needle files in various lengths and cuts from online jeweler's supply houses.
When files do wear out, have them "resharpened" at Bogs Tool:
http://www.boggstool.com/page18.html
By an "Opti-Visor" magnifier visor. It's the best and you'll wear it almost all day for years. Mine is still going strong, and I got it in watchmakers school in the late 1960's.
To determine what focal length, sit at a bench with some work held at a comfortable distance.
Measure from the work to your eye. Buy that focal length.
If you can afford it, pass on the Dremel and buy a Foredom Flex Shaft with a #30 keyed chuck hand piece.
Buy the more powerful unit.
Buy Cratex rubber bonded abrasive shapes and the appropriate mandrels.
The most useful are the 1/2 inch diameter "bullet" shapes, and the one inch diameter by 1/4 inch thick wheels.
Buy in various grits.
Buy the Dremel sanding mandrels and plenty of replacement abrasive drums.
Buy two vises. One large and one small part vise. Buy the best you can, but most are going to be made in China. The more adjustable and flexible the better.
Here's an ideal small part vise for fine work. It's the 2 1/2 inch Table Swivel vise.
https://www.harborfreight.com/2-1-2-half-inch-table-swivel-vise-97160.html
Don't waste your money on a Pana-Vise or any of the other hobby shop vises.
These are made of aluminum and don't hold, and the vacuum types don't stay put.
There's this popular picture of a gunsmith standing over a large milling machine or lathe making an intricate part.
The truth is, the vast majority of a gunsmith's time is spent sitting at a bench with screwdrivers, punches, and stones working on some assembly.
Since that's where you'll spend most of your time, make it as sturdy and comfortable as you can, with plenty of light overhead and a good bench light.