Thoughts, worth every penny:
If you are on a budget (and who isn't?) I would suggest prioritizing a set of good sharpening stones, both good sized bench stones and a slipstone or two for honing the inside of gouges, over lots of carving tools. You can get by with wet and dry sandpaper on glass (the Scary Sharp method) but with the price of sandpaper these days good stones are probably more economical in the long run. I have Japanese waterstones and like them for bench chisels and planes, but the smaller chisels and the gouges used in stocking and decorative carving quickly wear grooves in them, so Arkansas/oilstones or diamond stones are probably a better choice.
If you are going be buying vintage tools of ebay, a 220 grit super coarse diamond stone is a good investment for repairing damaged or poorly sharpened edges, changing bevel angles, etc. Slower but a LOT more controllable than a grinder. Generally a good investment anyway, but vital for refurbishing 2nd-hand tools, and handy if you ever try making your own chisels as well...
Speaking of which, a basic knowledge of heat treating, a piece of 1/4" drill rod, and a propane torch allows for making small chisels for specific tasks - I have a 1/16" mortising chisel I made for chiseling out trigger slots, etc., that has proven very useful for other things as well, like squaring up tang holes in knife handles. You might not want to start off by making your own, but that might be an option to think about in the future.
A good square is worth its weight in gold. I have a 6" machinist's square that I use for everything...
When looking over tool lists, bear in mind that carving a gunstock from a blank and relief carving a gunstock for decoration are two rather different tasks with different tool requirements. The latter can be a lot more tool-intensive depending on how you approach it. When folks are asked what is needed to make a gun, sometimes they include relief carving as part of the job and sometimes they don't, I think.
