I find that alchemy is really lame in Skyrim. It was much more effective/useful in Oblivion, imo.
You can make fortify enchantments, which are permanent, negating the need for fortifying potions.
Restoration magic is much, much more effective and improved over Oblivion, making health potions much less of a necessity.
The only really nice thing about alchemy is that if you spend enough time at it, you can make fortify enchantment potions, and create armour that fortifies alchemy. Wearing this armour, make more fortify enchantment potions, and repeat. This allows for some truly insane enchantments, but is really more of an end-game/for fun application of alchemy.
and the best way to train enchanting is to train your smithing by making iron daggers, then enchanting and selling them all.