Okay, here's the way to get the best possible enchantments:
Get 100 alchemy (creating the most expensive potions, they offer more alchemy xp) and get 100 enchanting (again, create the most expensive items, banish daedra being the best enchantment for value).
You also need to put 7 perks into alchemy (just the ones that benefit potions), and fill up the enchanting perk tree (you can leave out the far left branch if you want, the elemental enchantments only affect weapons).
Once you have both skills to 100 and the perks placed, you want to go to the alchemy table and create 2-4 "fortify enchanting" potions. Take these up to the enchanting table and pop them, giving you 30 seconds each to enchant headgear, clothes, ring and necklace with the "fortify alchemy" enchantment. This gear will become useless very soon and you'll sell them so don't use anything good, just a silver ring, silver necklace, basic clothes and a leather or hide hat.
ALWAYS USE GRAND SOUL GEMS! If you can't find enough mammoths to fill the gems, don't worry, just buy them and wait 48 hours in-game and the wizard of your choice will have them to sell again.
So now you have the alchemy gear, you need to wear it and make another set of fortify enchanting potions. You then head up to an enchanting table, pop the potion and create new alchemy gear. Now you need to repeat this and I'm not sure how many times, but suffice to say the absolute maximum alchemy bonus on clothes is 29%. Once you have this, sell all the gear that's less than that bonus percentage. You'll be able to see the bonus before you press "craft", at that point it's a good idea to rename the item to "alchemy clothes" or "__...of alchemy".
So now you just wear this gear whenever you make an enchanting potion and I think the bonus ends up being +130% enchanting. This is without a single cheat, the game designers clearly wanted this to be available, and if you find yourself overpowered, wear different gear, it's your choice ;)