I am an amateur home woodworker as an occasional weekend hobby, which I got into by starting to re-handle my own knives. I am set up in our garage. Now I am a big fan of Paul Sellers, who has lots of helpful videos, books, blog for new woodworkers. I have headed down the path of preferring hand tools (mostly) rather than power tools. I mostly use hand saws, rasps, files and sandpaper for my handles. You will need a workbench and vise as well. I did get frustrated with a cordless drill for installing pins and corby bolts straight and did get a proper drill press. I do also use a dremel or a hand held 3x18 belt sander secured in a vise on occasion. A shop vac handles my dust well enough. Most will tell you you need a long thin belt sander which could be helpful, but for my pace and occasional work, I have not missed it. A small buffing wheel in my drill press or handheld drill works well enough for polishing.
So my list for handle making tools includes:
Marking/measuring: combination square, calipers, divider
Saws- some Japanese ryobas and another small fine saw, small dovetail saw, coping saw, jewler's saw
Clamps- can never have too many clamps of all shapes and sizes, and a good sized vise (on a sturdy workbench)
Shaping-small belt sander, dremel, a variety of rasps, files and sandpaper
Drilling- hand held drill or drill press to make straight holes with good depth control
Buffing- micromesh paper, small buffing wheel in drill press
I have acquired all sorts of helpful items over the past few years. The list goes on and on if you want to expand to larger scale woodworking projects: planes, chisels etc. there are lots of "starting out in woodworking" tool lists, but I found the advice from Paul Sellers most helpful. If you want to get power equipment you can get things like a bandsaw, long thin belt sander, tablesaw, buffer, lathe etc. I don't have the space or tolerance for all those machines. I am happy with my slow paced (mostly) hand tools. Good luck on your journey. Let us know what you decide to get. I have been very thankful for all the advice and knowledge I have gained here on the forum.