Here's a thought. Instead of a set of four moves, why not have "memory points" to distribute any way you want between as many moves you want, or something like that. With memory points, you could choose between having a lot of weak attacks, or one or two very strong attacks. You'd get "memory points" with experience. Additionally, you would get extra points if you win a battle using weaker moves, or, on the other hand, you could get bonus points to a skill if it's already a strong move (meaning you could focus on one move and build it up). I don't know what would be better there.
