sketch '6.7 Detecting sound' which lights up an LED when a Microphone Breakout Board detects sound.
A DC motor is simpler than a servo. A DC motor only requires 2-wires and should behave a lot like LED-brightness, except it requires more current. You should be able to use a transistor or MOSFET to amplify the PWM output and control the speed.
You might have to experiment to find the relationship of voltage-to-speed, and you might have to give it a voltage "kick" if you want to start it at slow speed.
DC motors run pretty fast if they are not geared-down. If you want a very-slow speed without a gear, or a very-wide speed range, a servo or stepper motor might be the way to go.