See, I knew if I opened my big mouth I’d have to answer a question. There are others who will have different opinions, and probably better advice, but here’s my take on basics to get you started. There are excellent lists of tools elsewhere on this site. Also, do a search on tools here and you’ll find a wealth of information from people who really know what they’re talking about.
If you are considering building a rifle you will need tools anyway. To upgrade a commercial stock in the white you’ll need less than if you were starting from a plank or a good precarve. You’ll need a few good screwdrivers, a few good quality chisels, a variety of rasps and files, different grades of sandpaper, a solid means to hold the pieces and a place to work.
If don’t have a workbench, and you do have the forbearance of your significant other, a vice that clamps to the kitchen table will do the job. There is an active thread on screwdrivers. It has good advice, but a kit like the GPR won’t have tapered slots, so think accordingly.
One of the chisel kits with a variety of woodcarving chisels at a craft or home store might be good enough to start with. You will need a stone to keep them sharp. Also a regular ¼” and 3/8” chisel. A coarse and a fine rasp, and a coarse and a fine file.
This might be enough to get you through something simple. It is not exhaustive, and is not enough to handle any more than that. My intention is to get you enough to see if you like doing this without spending big bucks. Because you can spend big bucks, and not enjoy what you’re doing, and lose the forbearance of your significant other.
I hope others jump in here and help point you in the right direction, because there is always more than one way to skin a cat. And for advice on what you should do to make a GPR-like kit better you’ll need input from some other people anyway.