Geared motors are simple: A gearbox bolted to the shaft end of a motor. Industrial/commercial gearboxes are typically used to reduce the speed, but increase the torque in doing so.
However, lathe's speeds are adjustable for good reason. So, if you choose a geared motor, it MUST be modulable by way of speed. Typically, wood is going to require higher speeds, whereas, metal (Alum or brass) will require lower speeds BUT at high torque.
Too, I have never heard/seen a lathe that can be used interchangeably (with wood vs metal). Metalworking requires solid mounting surfaces with turntables, XYZ adjustments, reversing, etc..... where as wood is simple and far less complicated.
Too, metal requires cooling/lubricating oils applied while milling. You might find the cutting oils stain any wood working you might perform.
In any case, I would choose a DC motor. They are WAY easier to modulate their speed than AC. With a DC motor, you simply modulate the DC input voltage, and the motor's RPM will respond accordingly. Your variable power DC supply must be able to sustain increased currents at lower voltages as the motor will still have to produced rated HP at a lower voltage.
Good luck.
