I am looking in to making a UAV quadcopter and I don't know how to calculate what ESC to use with the motors I have picked. I am looking at buying the HobbyKing Red Brick 10A ESC and the Turnigy Aerodrive SK3 - 2118-3100kv Brushless Outrunner Motor. Will these work together? Is it overkill? What battery would I want to use that will be light but have a long battery life? Is it the most efficient it can be for the price and application? If anyone has personal experience or knowledge in this all input and ideas are welcome.
They should work, and as the info on the motor page states, you should use a 2 cell Lithium-Polymer battery.
A good calculator can be found here, it will let you know how much you can lift, run for, etc and should help you find the best propellers and best capacity and required discharge rating to use.