If childhood taight me anything, the minimum is just 2 buttons. Forward, reverse-left. Simple, usually effective, and maddenly oversimplified. I think I liked the one that only sent forward more, but it of course required a track.
People forget simple things like steering servos were not available to most kids until the 90s injection molding explosion that is so ubiq today.
Weren't there single-button ones that would continuously drive forward unless you pressed the remote control button, which would switch it to reverse-left?