RE: Battery Size? What is next?
Put it on an airframe and fly it using one of the suggested prop sizes. Evaluate flying performance against what you are looking for. Try a more aggressive prop for more power and be sure to check amps/watts with a watt meter to make sure you wont go over the limits of the esc and motor. That setup should be a good starting point. If your flights only last a short time, you might want to go to a larger battery.