RE: Li-iPo Batteries
DO NOT use the 1500mAh pack until you identify it and find out what its C rating is. The pack you save will be your own.
It's not the size of the ESC that determines the Amps, it's the design of the motor, the size of the prop, and the voltage from the battery that determines how many Amps are drawn.
As he said above, the ESCs are more than adequate, BUT, the motor will draw too many Amps for any of those packs to handle individually. A 300 motor system generally draws around 8 Amps. Your 1300mAh packs will only handle 3.9 Amps. The 300 motor will wreck them, unless you parallel multiple 2-cell (2S) LiPoly packs together to get a capacity of at least 8 Amps.
Those 3S LiPoly packs have too high a voltage for the 300 motor. It will burn out quickly. Don't use them.