With my archer character I have no issues with leveling up my skill. I shoot at every mob and boom, it goes up.

On my mage, I'm at level 14 and already starting to see mana issues. I haven't gotten enchanting up high enough for a 25% reduction (I think I have 1% (lol) on a piece and then a 12% robe I found. Also, in trying to cast a Familiar and then a Soul Trap I almost OOM at that point and can't really burn into a mob with flames or spark. And my destruction is only at 22.

Outside of training what else can I do? I don't have the tree perk for apprentice spells and I'm not sure if I need that once I get the mana reduction enchants. Should I get the next spell in the book (apprentice level)? Would a "more powerful" spell help me level faster there?

Level up magic skills on summoned creatures.

Get the apprentice perks. Familiar and soul trap are both apprentice spells as I recall.

And heck, if your destruction is only 22 at 14, that's pretty ridiculous. That's 13 levels, but only 7 skill gains.

I agree Tale. That's one concern I have. Between casting Familiar and Soul Traps it seems impossible to level everything up...lol.