This just so happens to be my specialty . . .
So first, you need to calculate how effective your robot will be with these motors. Its nothing to be subjective about when your expensive robot is at risk
For a battlebot, high acceleration is best.
Secondly, since a round is only a few minutes, who cares about battery life - just buy a few and charge them all. Swap them out after each round. Instead of getting high capacity batteries, use that weight for better armor.
Finally, you asked about current. Look up the datasheet on the motor. It will tell you required current draw vs output torque (which you calculated earlier). Knowing current draw and voltage of motors, you can calculate what batteries you need. For example, if a motor requires 10A of current but your NiCad batteries can only handle 6A, then that means you need two in parallel, etc. Knowing current draw, you can determine exactly how long your batteries will last, too.
Ive seen batteries fry during these competitions because people dont bother with these calculations . . .
let us know how you do!