First of all, you don't want to be designing circuits that will fry when connected to an ideal battery that can supply unlimited current. The circuit itself should be designed so as not to draw more current than it can handle when supplied with the proper voltage. The only battery spec you should care about from a circuit-frying perspective is voltage. The battery specs you care about from a performance perspective are mah (how long will your battery last), current (can your battery supply as much current as your circuit will need), and noise (a noisy power supply can cause your circuit to behave erratically, though noise is not usually much of an issue for batteries).
So in short, mah only matters if one of your requirements is that your robot be able to operate for X hours drawing Y amps without running out of juice.
