Can you just take a cheap remote control car apart and mount your disk to one of the wheels and use the existing controls? How big does it have to be? How fast does it have to spin?
No point reinventing the wheel.
Our kids have these
Morphibians, and their wheels go forward and reverse with existing controls.
edit: I missed the part about continuous speed adjustment. Not sure how continuous the speed adjustment is on these. A drill will do all that though.