I'm sure you've gotten enough good advice. But I'm gonna throw my own at ya', anyway ...
I have a shop full of power tools. I did a bit of carpentry level projects through the years, and I thought I was pretty good. Then I was introduced to the world of vintage woodworking, and was blown away. Over the last 3 years or so, I've goofed off in the shop, playing with dovetails and other joints, all using chisels and hand planes. I also got a lot of satisfaction from finding a vintage tool and re-fettling (refurbishing) it to working order.
I swung in the direction of vintage, and found that it's a really enjoyable experience. "It's about the journey, not the destination" really seems to ring. It takes longer, but I think it's more satisfying.
As far as what you need for vintage ...
- You certainly need a good sturdy bench. Other posters are correct; if your table rocks or bounces, it's gonna mess up your process. Paul Sellers shows how to build a good bench. And once you have that, the rest seems a piece of cake.
- To make life LOTS easier, you'll want to invest in a woodworking vice that will attach to your bench. This is probably one of the biggest expenses you'll probably make, but it's seriously worth it.
- 1/4", 1/2", 3/4" and 1" chisels. You can go cheap to start out, but no matter how much you spend, you'll need to learn to properly set them up (flatten the back, and square and angle the bevel).
- A hand plane. #4 or #5 size. A cheap $5 flea market find can get you going.
- A way to keep your edges sharp. A thick, flat piece of glass or tile, with sanding paper (150, 220, 400, 600 grit will get you started.) Later you can move to water or diamond stones if you wish.
- A wooden or rubber mallet for bench and chisel work. No, not a metal hammer, as they're too heavy for fine work, and can damage wood-handled chisels.
- A combination or speed square. You'll want to ensure it measures as close to 90 degrees as possible.
- Measuring tape. Big ones are ok, but I get along great with my 9ft tape on my bench. Never needed any more.
- Clamps. At least four 2-3 foot bar clamps, and a couple of spring clamps.
Other than the cost of the bench build and woodworking vice, you can probably pick up most of these tools for less that $100-150. Once you're feeling a bit more comfortable, you can start investing in more expensive tools.
Good luck!