The very first lathes were called pole lathes, and could be constructed out of some wood, a gouge, a chisel, rope and an axe. Your lathe, on the other hand should probably be less difficult to create. The best wood lathe should have all of these: cast iron bed, tail stock and head stock, secure and convenient locking, four speeds, dust proof motor, a good dealer who will be around when you need spare parts, spaced bearings that support the spindle well, and about a dozen other things. Combine that with the best wood chisels you can find, and you are ready for action.
Try to avoid ones with light sheet metal construction. Your best friend when it comes to a lathe is one that doesn’t vibrate. You just want it to spin, not shake, and the heavier it is, the less it will vibrate. You want one that is massive and rigid for the best effects. Cast iron will give you the most weight per metal. You want the most dense for the size of the project. A giant lathe capacity will be really awkward to use to build an elegant pen on. Don’t sacrifice the quality of the engineering, the weight and rigidity to get a big capacity if you’re not going to to need it for a specific task. Most projects will fit just fine with a ten inch to twelve inch swing over the bed and thirty six inches between the centers.
Other than the lathe, you will need a bench to go with it, a set of tools, safety equipment, abrasives and polishes, sharpening equipment, a workshop–and wood. There is a lot of information on how to turn wood, where you can get free wood and what you can do with it. Always have a face shield to protect your face and not just your eyes. The little safety glasses do not cover enough. Wear a mask to prevent inhaling the dust. Between all of that, you should be ready to practice on wood blanks.