The longer I build guns, the fewer tools I realize I need. When I built my first rifle, I had very few tools... A couple of chisels and a few files. And thinking about it, that is really all you need to get started. That gun is what I refer to as a "Kitchen Table" gun, because that was my bench at the time, much to the chagrin and disdain of my wife and Mother-in-law. Regardless, that is where I built it slowly over a period of 2 years. No vise, no bench, no jigs and worse, no idea what I was doing. But I did eventually finish it, and as hideous as it is, I keep it. It is not that my workmanship was bad, but my ignorance of architecture made it an ugly thing.
Now this was not the fault of my lack of tools... To the contrary, the inletting and fitting are really pretty good. And it only took me a minimum of tools. I had a set of 5 palm chisels, a 1/4" straight chisel, a jeweler's saw and a few files. Yes, I did relief carve it, thus the reason for the palm chisels. Also needed the palm chisels for inletting too. But really, you don't need many tools if you are not doing any forging or casting of your own parts.
One thing I would highly, highly recommend is a few good stones for sharpening and making a strop for them. These I consider absolute requirements. You must have sharp tools to do this type of work. And you must learn to use them properly. I really can't emphasize this enough. Dull tools not only cause accidents, but slow you down.
M. E. Pering