A 4 channel radio will fly 90% of the planes out there. Gives you aileron, elevator, throttle, rudder. The 4 basic flight controls.
You would need a 6 channel or more if you wanted to experiment with things like flaps/flapperons/spoilers/spoilerons, retractible landing gear, bomb release mechanisms, actuated canopies, transmitter operated kill or choke for gasoline engines (optional, always), etc....
The difference in price between similar 4 and 6 channel radios is usually low, in the 20-50 dollar range. I think it'd be money well spent.
If I were starting today, I'd be looking at 2.4ghz systems, to avoid having issues with frequency control, but if you're on a budget, a 72mhz system works great and saves 50 bucks or so.
If you're gonna go 72mhz, it pays to contact your local club and see what frequencies aren't in use there. That can help avoid being the 3rd flyer on channel 43, like I am
J