Enchanting would seem applicable to all types of mages. Those mages specializing in necromancy or conjuring would probably be more inclined to enchant things, since soul trap is in that magic school. But pretty much any mage could reasonably enchant - from a role play perspective.
As mentioned about enchanting is to mages as smithing is to warriors.
Personally I would tend to not have a Mage get good at smitthing. My current level 61 mage will never smith anything or mine anything -- she thinks the manual labor is beneath her. On the other hand my warrior characters would tend to not enchant, thinking it is not exactly honorable. That way I avoid the over poweredness of using both crafting skills. That is just my (current) opinion.
The third crafting skill (Alchemy) is in the stealth school. I love Alchemy so much I use it with all characters. But I tend not to put perks into it except for stealth based characters.