Hey Kaine, you cannot use two motor shields stacked together since it would be using the same pins and interfere with each other.
You can use 3 of these mounted on a board but will have to make a special board using them: http://www.jayconsystems.com/tb6612fng-dual-motor-driver.html
Servos would be a better option. You can easily control up to 12 servos with the basic Arduino. You wont need to buy a special shield for Servos but you will need to make a board to connect the signal wires from each servo to the Arduino and to supply power to all the servos.
Hope this helps!