My tool list for a beginner gunsmith is knowledge.
Not just how to work on guns but learning how to silver solder,heat treating spring steel with torch, rust bluing, when to do something and when to stop doing something ect. I would look at purchasing books and YouTube videos. One of my favorite is Mark Novak anvil gunsmithing.
Besides knowledge you will need a small 2-3 oz ballpeen hammer, rubber malet, a good set of gunsmithing screw drivers, bench vise, pin punches, a propane torch,
Tap handle, small needle file's, and a medium mill file. if you have room a drill press and 12 ton press that you can use for removing barrels with wooden blocks that you made with a drill press. As you go along you will be buying tools as needed . That may be a list more for a gunsmith than a hobbyist. It all depends on what you want to do and how far down the rabbit hole you want to go.
Good luck have fun and never put your fingers where you wouldn't put your manhood. I mean stay safe.