And quickly because I hate all crafting. It's so boring to me but I want to attempt a Mage character who won't be underpowered like all my other ones.

Get rich.. Then buy a lot of soul gems.. Azura Star is too slow to be useful..

hoard weapons and then enchant them with "banish"

go to kolskegger mine, smelt the gold ore you can get there, and make 50+ gold rings with it. enchant them with fortify sneak.

There's a point in the game where you start having trouble finding merchants with enough gold to sell all your loot to. If you buy filled grand soulgems off of them it balances out and you can use the grand soulgems to enchant your stuff.

Buy petty soul gems. Get a weapon with soul trap and the courage spell.

Cast courage on deer, they will run right for you. Now kill them, and make items. Yes it is crafting, but it is also the fastest way. Horkers are also good because they are normally in packs of 3 and all along the northern coast.

Weapon enchants normally earn more profit than armor enchants. Banish is the highest, but absorb health and turn undead also net good returns and you will find those at lower levels. If you have weapons, enchant them, if not make iron daggers and enchant those. I'm not saying this for raising smithing, I'm saying this because iron daggers are so cheap to make. Especially if you have been killing deer which will give you all the leather straps you will need. An iron dagger will cost <10 gold to make, the petty gems will cost 30 gold I think, and you will be selling enchanted daggers for 100+ gold a piece. Use the profit to buy more gems and better enchantments.

Disenchant everything you don't plan on using

You could technically wait until you get daedric equipment in random chests and disenchant only those. At very low enchanting levels disenchanting one will raise the skill by few points at once. It's not exactly viable, though.

Weapons with one second long soul-trap enchantments are great.
They never run out of charge, and the souls are always captured.

trapping? no no, that takes way too long. there are a lot easier and faster ways to accumulate charged soul gems.

hidden caravan chests, blue palace merchant chest, steal them from the college, and if you must you can farm them from spiders and spheres in dwemer ruins.