Thanks for the advice! I'll give 3S a try, then. It has the advantages of being unlikely to explode the motors, and also means I won't need to buy a new charger.

With that in mind, I've done a bit more interweb shopping, and have bought:
A Zippy 850mAh 3S LiPo
Some Vex 29 controllers
A 500RPM weapon motor

Now I just need wheels (might use Lego), and a BEC for the RX.

oh, and the body of the robot..