To build a plane you have to have some idea of what you are trying to accomplish in a hundred things that need doing in construction. Go find a kit or buy mail-order a kit. Build some kits of planes you can manage. Simple planes, then more complex ones. Build from plans when you know you can handle it. There will be a dozen problems to solve that you will have to figure out on your own. Experience from kits is the only real way. If you cannot afford to buy decent plans you certainly cannot afford this hobby. Subscribe to "Fly RC" and "Model Airplane News." They are not expensive, they are full of information and ideas and the advertisements are listings of the parts and assemblies and plans and kits that exist and can be bought at a hobby shop or by mail to solve problems you cannot even imagine until you have to solve them.
Minimum building space is probably like the setup I use. I have been building balsa airplanes for 60 years. Continuous low-key effort. I have a table from Wal-Mart, fiberglass with folding legs; a storage rack made with 1 x 2's from Home Depot, total space 3 ft by 8 ft and 8 ft tall. Cost about $200 total for table and rack. In building the kitchen table will not work because it will take days or more likely weeks and probably months. Continuous process. Foam kits and ARFs are a lot faster.
Lots of big expensive power tools are very nice. Us ordinary mortals get by with hand tools. You need a couple of Exacto handles and a substantial supply of (#11) blades. A large flat file (shaper); a supply of sandpaper and some wood blocks to serve to hold the sandpaper. Hand tools- 6 and 8 inch needle nose pliers, a couple of hemostats in different sizes, a medium size ball peen hammer, a razor saw and two or three screw drivers of phillips and flat tips, an allen set in inch and one in metric, water pump and channel lock pliers, about a 100 T-pins from hobby or fabric stores, Saran Wrap, blue painting tape, a kit pack for electrical work that includes a crimper tool and a decent small soldering iron. Make sure any solder you buy is 60% Tin and 40% Lead and not the other way around and it has a rosin core. You will need a propane torch and buy silver solder as a small kit from a model airplane hobby supplier. Find propane cheap in a camping supply place. Buy a Coleman propane lantern while you are there for emergency lighting. I bought a bottle of Propane last week at Wal-Mart for $2. Another brand of the same stuff on the same shelf was $7. For tools and a box for them check Harbor Freight. A Dremel or similar rotary tool will help. An electric drill is required. Razor plane from the hobby supplier. You really do not have to buy expensive pretty things like a $150 Flight Box to build good airplanes. Just buy decent plans, good balsa and parts, and use decent tools made to do what needs to be done. A couple hundred dollars worth of tools and supplies will get you to where you can reasonably start to begin to build from scratch. Kits are actually a little cheaper but the same tools are pretty much still needed. Foam ARFs can be done (sometimes and according to the manufacturers) with bare hands and maybe some special tools included in the kit. Ultimately there is no end to the list of tools or supplies and the ones mentioned above are only an idea of the minimum to get by.