>>893433You can make a lathe capable of turning metal from mounted bearings, stable (thoroughly dried) wood, and any linear slides you can get your greasy hands on. If you are in it for the process and not for the products produced, a watchmaker's style lathe might be appropriate. You use hand-held 'gravers' resting on a tool rest, instead of a tool held by a toolpost guided by linear bearings. You could also make a cylindrical grinder type arrangement, which doesn't need to be nearly as rigid to hold tight tolerances. By turning and grinding components mounted on the spindle in their final position (chucks, pulleys, bearings), you can build accuracy as you go.
I bought a cheap Chinese lathe recently, and I am already trying to get rid of it. I would have been much happier with a lathe I made myself, even if limited in capability. My other lathe is a Taig which is thoroughly modified and a never ending project. While it isn't very rigid, it's very capable. I feel good using it unlike the chinese lathe.
Good luck!