if you're okay with having to look closely at people's character sheets, but want a system that is easier for players to comprehend, You could try making some simple rules for circles of magic and then have players choose the ones that interest them the most.

One example of this would be having something akin to avatar, where everyone is a single element. Though you would be required to detail this a bit so that you could make the appropriate calls when the situations arise. Is lava more of an earth power, fire power, or both? Can water benders manipulate things that aren't 100% water but mostly water, like all organic life? What prevents an air bender from forcing air so hard into someone's lungs they over inflate and explode? 

Maybe you want to give people the ability to make more unique forms of magic, but still have an underlying theme for the RP. You could have very basic schools of magic that the player's magic would have to abide by. As an example, maybe the "destruction" school lets people create powerful forces to crush their opponents with, but not actually make anything. This would let a mage fling fireballs, bolts of lightning, and even ice spikes. However, they wouldn't be able to do anything defensive with their magic like make barriers, or fortify weapons or armor. You'd need to come from an "enchanting" school if you wanted to enchant things, or a "manipulation" school if you wanted to change the elements in your environment into barriers and the like. If you had enough schools, it might even be possible to let players pick two or three schools for even more diversity.

As for governing combat, it really depends on what you want out of it. If you want to write exciting fights, I say do free form. But if you want it to be more like a game where the excitement comes from playing against another player or entity, you'll have to look at tabletop mechanics or figure out your own rules.