That sounds like a fun project. Since your post is less of a detailed write-up of your motor and pulley system, and more of a general query about what products to use to motorize and stabilize that system, I moved it to the General Robotics Discussion sub-forum, which is a more appropriate place for asking those types of questions.
It sounds like you might not have a motor driver or motor controller in the system you described. If that is the case, and you tell me more about your motor, like its stall current and operating voltage, I might be able to recommend an appropriate motor driver. In general, you can control our motor drivers directly from programmable controllers like the Arduino Mega, which can also read analog voltages from joysticks.
You can find all of the inertial sensors we carry, including gyroscopes, here.