making a variable pottery wheel drive would only involve mechanical work using any kind of motor strong enough to keep the "turn table" rotating with the heaviest load planned to work on.
A good motor is a brushed AC-motor as used in add-on sewing machine drives. They are normally fitted with a foot pedal operated speed controller.
All you have to do is fitting a belt from the motor to the bottom side of the pottery wheel.
Another solution with a fixed rpm motor is a so called "ball-disc-integrator".
The entire drive is mounted underneath the wheel and is variable in relative position to the center of the wheel. A small toy car wheel (rubber tire) is mounted to the motor shaft and drives the pottery wheel by traction. The further you move the drive towards the center of the wheel the slower it will rotate. You can do this by almost centering the drive with the pottery wheel. Keeping the minimum position spring loaded you might use a foot pedal and a bowden cable to move the drive along the entire radius to gain maximum speed.
This method was also used with some of the first cars on this globe since a transmission box was not invented yet.
Having no restriction on the bottom of the pottery wheel you might even reverse rotation by sliding the drive to the opposite side of the center - of course with a full stop at the center and slowly increasing rotation speed beyond it.