I have posted info on the tools I use, but I have never gone into much detail. This post will cover the tools I use and what you should look for when it comes to gun specific tools.
First I should remind everyone that what I do is not really gunsmithing, I restore guns, I do not machine them, I do not make guns or gun parts.
I am more of a gun restorer or gun mechanic.
The first tool(s) every gun owner should own is a good set of gunsmith screw drivers. What makes a gunsmith screw driver different from an ordinary screw driver is the profile in which it is ground. Gunsmith screwdrivers have what is known as a "hollow ground" profile. This does not mean the center of the screwdriver is hollow, it is a term used in knife making to describe a grinding in which both sides of the blade are parallel at the edge rather than a continuous taper, the picture below explains what I mean:
using standard screw drivers may cause them to slip out of the groove and damage the screw heads, fortunately they can be repaired, see my post about it here
You can buy a dedicated screw driver set like this one from Pachmayr
or one with interchangeable head like this one from Wheeler
Other important tools for anyone hoping to work on guns is a good set of punches. You will soon find out how many guns use pins to hold their moving parts in place, you will want both brass and steel punches, be sure to buy good quality punches as many the foreign made ones are often of poor quality. This set from Wheeler is pretty good
If you plan on doing tear downs on S&W revolvers and other guns that use rounded pins, you will want to get some special "cupped" punches, these protect the round edge and keep the gun looking factory fresh
Brownelles sells these special punches
As does Midway USA
Besides the disposable tools like sand paper, naval jelly, bluing solutions rags etc... you will also want to invest in a good set of files. Large, small and needle files (for repairing screw heads) will be needed. I built my collection of files by buying them as I needed them. Again Brownelles and Midway USA are great sources for gunsmithing tools.
Finally a way to hold on to the guns and gun parts is essential. I use a standard bench vise with pieces of oak for protecting the gun metal from the jaws of the vice. Other people use leather or soft brass or copper to act as a cushion. Another good vice is a dedicated gun vice like this one from Tipton