The Mah of the battery does not matter. Mah is Millamps hours. This is basically a measurement of how long your battery can deliver power. The ESC doesn't care if a battery is 600 Mah or 6000 Mah. It's the voltage of the battery that matters. And that would be determined by the number of cells in the specific battery back, as is indicated above. 2-4 cells for Li-po (or approximately 15.2 volts for a 4 cell Li-po), or 6-12 cells for a Ni-cad/Ni-mh (or approximately 16.8 volts for a 12 cell pack)

BEC = Battery Elemination Circuit.
This is what is used to power your receiver so that you do not have to have a seperate battery for the radio. It runs off of the ESC. The specs above mean that the BEC, or your receiver and servos, cannot draw more than 4 amps.

Ken