Go with something like the bitwhacker, as suggested, and use it to control relays, which are connected to the motors, controlling on/off (and change direction). The connections via the relays will be similar to how your instructor is using switches, the relays just replace the switches (he is likely using DPDT relays with center-off - you would probably want to use two SPDT relays, like Bosch automotive relays, for the same ability). The relays aren't directly controlled by the bitwhacker - you will have to interface them to it using an NPN transistor (look up microcontroller relay interfacing for details) - and remember your flyback/snubbing diode across the coil of each relay!
Once you get one motor working, you'll understand how to do the rest. At that point, you will need to figure out what to use and how to code the interface to control the bitwhacker (and how to read your USB controller, and interface with your camera). You should start with getting a single motor under control of the bitwhacker, with a simple interface (GUI or otherwise) that allows you to turn it on, off, and change direction. Don't try to do everything at once (that's a path to failure) - instead, break the problem up into smaller chunks, and if each of those seem complex, break them up into smaller chunks, until you have a manageable list of tasks and steps to follow to completion and success.
Good luck with your project!