As well as the required power, knowing the general type of motor would help, brushed or brushless?
ESCs don't care what type of battery is powering them, LiPo, NiMH, SLA, two coins stuck in a lemon, whatever. Its all electricity. If the chosen ESC doesn't have the ability to go into a safe mode on low volts, a separate warning circuit will be needed.
Cheap is not always lowest cost. Getting a cheap one then having to replace it with the real thing is more expensive than just buying the real thing in the first place.