Hey wings

It is not necessary for a trainer to have ailerons... and as Ballgunner said very large planes some even giant scale have rudder only, However the whole point of at trainer is to get you use to what you will fly in the future and that is the main reason most recent trainers have four channels.

As for your radio choice I highly reccomend the new Futaba 6EXA because it is very similar in price to your standard 4 channel radio but it is a computer radio with 6 channels capable of everything you would evr want to do with an airplane. I just ordered one yesterday and will tell you how I like it when it gets here

Balsa is much more durable than you may think for example if and when you do crash a balsa plane you just cut through the covering and replace the damaged wood whereas with foam you normally have to order a new part and a drop of regular CA on foam will melt right through it.
remember the main thing about flying is to have fun and there's nothing more fun than your first solo.