A good place to get started is construction lumber -- just 2x4s. They're not bad once you clean them up with a sander and potentially planer and finish them, and they have a certain industrial aesthetic raw. They're cheap enough that if you mess up or change your mind, you can throw them away and try again. And if you want to redo a piece of furniture, you can do that too. If you want to make a custom mount for something, just drill a hole.
Homes look surprisingly good when all the furniture is custom -- floor-to-ceiling wall-to-wall bookcases, desks designed for what's on them, etc. -- even if it's just cheap construction wood.
From there, you can move upscale. You can go quite far with Home Depot plywood sheets. Done well, they look great.
I have a mix of fine woodworking pieces (which take a month or two to do), to things which take a couple hours to throw together. And it feels awesome once most of the furniture in your home is handmade. And it's a much better use of space.
Get a few 2x4s, a pair of cordless drills, some nice screws, a circular saw, a carpenter's square, a tape measure, and safety glasses and you're good to go to get started.
If you want to step it up a notch, get a random orbital sander, proper guides, (GOOD) clamps, a router, and a jigsaw. If you can at all afford it, buy NICE tools. Better beats more. I'd rather have a good Bosch cordless circular saw and drill than a full kit of Walmart toolkit. And they'll cost less in the long run, with less damaged work pieces, and fewer broken tools.
Also, Youtube videos are great. So are online woodworking forums. Classes are nice if you can afford them, but hardly necessary.