[frizzen]

You're wanting 11v, so that's 3s lipo. 3s means 3 cells connected in Series. Some also add a P for parallel cells, 3s2p means 6 cells with 3 series sets of 2 in parallel.

mAh is milli-amp hours. It measures run time / usage. Your 4000 mAh battery has 4 amp hours of power. I can pull 1 amp constant for 4 hours, or 8 amps for a half hour. Your 2000 mAh battery has 2 amp hours of power. I'd probably start around 2000 or 3000mah, and see if it had enough run time for what you're wanting.

Lipo batteries also have a C rating. That rate of Change is how fast you can charge or dischange without damaging the battery. It has to do with how many times the capacity of the battery can be pulled out at once. Racers worry about having really high C numbers. We aren't going to pull on a pack that hard so stick with the cheaper packs that have the Volts and mAh you want.