is there a type of woodworking you were thinking about? Chip carving, figure carving and power carving in general have a much lower cost then typical woodworking although good knives are not cheap. Turning is a step up in price but still typically less then what most people think of as woodworking such as shelves, tables, furniture.
None of the below are mine.
Scroll sawing might be an option to consider. You could keep that reasonably priced depending on what you are wanting to do.
Scroll saw box:
Scroll saw bowl:
Scroll saw art:
If you are an artistic person you may enjoy woodburning or intarsia. I have watched people wood burn before and it was amazing watching the lion the guy was drawing using woodburning tools come to life. The basic woodburning tools to get you started should be reasonably priced and with the reach of many people. Also Intarsia combines art and woodworking. It can be done with just handtools although a few power tools would helpful.
Intarsia Art:
Chip carved clock: