Basic start-up tool list? : woodworking
I'm in a very similar situation. I've recently been drawn to pursue woodworking as more of a full-time hobby was faced with a similar dilemma as you. I already had some of the basic rough carpentry tools, (hammers, saws, drills, ect.) but none of the tools that would be needed for “finer” woodworking.
My specific tool needs were determined my own specific circumstances, and woodworking interests. Since I am young single individual who will likely be moving several times and living in small apartments for several more years, large power-tools were out of the question, and even some of the handheld power tools were ill-advised due to potential noise issues, as a result I went the had tool route; and since my own personal woodworking interests lean towards furniture making my choice of tools partially reflects that.
At present my woodworking toolkit consists of a #4 smoothing plane, tenon saw, coping saw, 4pc chisel set, combination square, sliding bevel, mortise gauge, chisel hammer, general purpose panel saw, a small assortment of clamps, and a set of sharpening stones. This is in addition to all the general household tools that you can find in every toolbox (carpenters hammer, screwdrivers, tape measures, pliers, cordless drill ect.)
With these tools I am able to tackle modest projects while I continue building my skills, and was able purchase them all for just a few hundred dollars (which as also a factor considering my income). While I could have gotten them cheaper by restoring vintage tools or going with slightly cheaper brands, I didn't want that added variable introduced to my woodworking of having to worry about my tools functioning properly. By starting off with good quality tools, I can focus on improving my technique rather than worrying as the tools. In the future I will likely go the vintage tool route once I am confident enough in my own skills to be able to worry about restoring vintage tools.
Going forward I am planning to purchase a couple more tools to round out my basic toolkit such as: a hand router, spokeshave, cabinet scrapers, and some shaping tools such as rasps and carving chisels/gouges, oh and of course clamps, I never have enough clamps.
When planning out my toolkit, one of the big influences was Paul Sellers Blog I really like how he emphasizes being able to do complex projects with only a small number of tools. His concept of Ten Hand Tools, Three Joints was especially helpful as a starting point.