Currently, I'm having some kind of "trouble": I don't know how would I like to make characters to grow in power. I'll present you with some possibilities.

Governing Stats
Levels
The most popular method of raising stats: you fight with enemies who drop Experience Points (EXP) and after accumulating enough number of EXP, a character gains a level and all his stats raise. Being the most popular, it's pretty "unoriginal".
Consumable Items
Perhaps a bit rarer method of governing stat growth is by using items found as loot from enemies, from sidequests, or obtained from chests is to use and spend an item that governs a stat and raises it.
Sphere Grid/Licence Board Mix
I could also go through the trouble of eventing quite large map on which there would be various slots on which the player would spend points earned from killing enemies. That is possibly on of the rarest views in RPG Maker games.

Governing Abilities
Levels
This would require using the "Governing Stats-Levels" method to be used simultaneously: after reaching a certain level one or more abilities would be learned. Once again, being the most popular method, it's pretty "unoriginal".
Consumable Items
Would go well with "Governing Stats-Consumable Items" methods where governing learning abilities would be by using items found as loot from enemies, from sidequests, or obtained from chests and spending the item that teaches a certain abilit to teach that ability.
Sphere Grid/Licence Board Mix
Once again, I could also go through the trouble of eventing quite large map on which there would be various slots on which the player would spend points earned from killing enemies. That is possibly on of the rarest views in RPG Maker games.
Equipment Learning
Learning ability from an equipment piece; could only be used after mastering it, similarly to Final Fantasy X-2 ("usable after mastering" piece).
Equipping Auto-Abilities
I also consider equipping auto-abilities similarly to Final Fantasy IX: you have certain amount of Capacity Points and the player needs to assign auto-abilities according to available CPs and additionally to skill slots of which limit could be increased.

So please, state what you want to see.