20 minutes is a looooong time. You'll be tired before you've flown half that long, especially just getting started. You can buy a charger and more than one battery pack so X minutes of flight time doesn't mean "fly X minutes and go home".
AA batteries in the transmitter is OK. In the plane alkalines will get expensive. However they may be used to power the receiver. There are also AA size NiCds for small planes.