[KenWittlief]

If the purpose of this project is to build something with the information you are learning, then they may not allow you to use Radio Control systems from RC cars, or VEX controllers. They may require you to use pots and wires to power the motors

you could still have something like a tank turrent spinning on your robot, if there is a non-spinning surface on the top for the control wires to exit the vehicle upwards.

BTW: For Sumo cars (competition where the car at the center of the table after 1 minute is the winner) fast is better than slow and torque-y. When two sumo cars are in a pushing match there is only so much force (energy) at your disposal. But if your car flys across the table and smacks the other one, it will send it flying (impact and momentum). Usually it will knock the other car right off the table.