What sort of woodworking do you want to do?
How much space is "limited space"?
Either way, any tool kit should include:
-Cordless drill
-Circular Saw
-Hammer
-Philips Screwdriver
-Flathead Screwdriver
-Ratchering socket wrench
-Channel lock wrench
-Adjustable wrench
-Needle nose pliers
-Standard pliers
-Diagonal cutting pliers
-T-square
-Level
-Measuring Tape
-Sanding blocks
-Pocket knife
-Putty knife -Rags
-Drill bits and screwdriver bits for drill
-Socket sets for drill or ratchetMost of these hand tools can fit in a toolbox, and the power tools won't take up a ton of space.
For the power tools, you want something reliable, but do not feel the need to break the bank. I'm partial to Milwaukee brand tools, but I've also used DeWalt, Makita, and Ryobi, and cheaper brands I wouldn't recommend. Ryobi is on the cheaper side, but I have had good luck with their tools. I prefer cordless, but a corded option is cheaper and probably more reliable if you have a good workspace and plenty of outlets.
For the hand tools, cheap Harbor Tool stuff is probably OK to start. When they break, that means you're using it enough to justify getting a nice one. You can also surf your local Facebook groups for free tools people give away sometimes, or check your local Goodwill shops. Used tools can be worn down or broken, but most of the time it's just old.
Second-level woodworking power tools you shouldn't buy until you need one:
-Jigsaw
-Orbital sander
-Router
-Biscuit joiner or Planer
-Rotary tool (dremel or similar)
-Reciprocating saw
-Impact drill or driver
-Dedicated screw gun
-Nail gun (and compressor) -Angle Grinder (mostly for metalwork)Larger items that take up space:
-Saw horses
-Workbench and Toolboxes
-Table saw
-Routing table
-Drill press
-Band Saw
-Planer
-Compressor
-LaddersHand tools for specific tasks (buy when needed for a project):
-Paintbrushes
-Hand planer -Tin snips
-Rubber mallet or specialty hammer -Drywall tools
-Tiny screwdrivers
-Allen wrenches/keys
-Pry bars
-ClampsEdit: I almost forgot safety gear.
-Work gloves
-Safety glasses
-Ear muffs -Dust mask -Hardhat and reflective vest (if you're working on job sites)If you're in a big enough city look for a maker / hacker space.
Pumping station 1 in Chicago is one of the bigger places. It has like a half dozen table saws for 65$ a month. That's on top of 3d printers, other woodworking shit. Place is fucking huge. There's a virtual tour on their website. Just cool to look at all the shit even if you're not in Chicago. Gives you an idea of what a maker space can be.
Otherwise, some wood shops rent out time.
Either way is a great way to build a network and get started.
Some of the discussion would need some sort of budget honestly. That and just how much space you are willing to allot to this. You can get away with a really small space with a small to medium workbench, a couple bench planes, hand saws and chisels, but not everyone wants to deal with hand tools. Though this is the most space efficient.
If you want to save space, you can always get s3s or s4s lumber (though personally I would still use a bench/hand plane to reflatten to lumber) but that increases each project cost.
If you give a rough budget, space, and even potential project list, I think a more tailored purchase order can be given.
