Mages' Guild was okay in Morrowind, it's just that magic wasn't all that interesting to use. It was much better in Oblivion and pretty good in Skyrim.
I haven't actually tried making a wizard type because I've always had a melee type character, I plan on trying it anyways.
While I usually went with tank-types, I never bothered making a mage character at all either. They didn't seem that fun to attempt, like they would die often or something.
Oblivion is especially class fluid. You can make an assassin or a paladin and still have a good mage. It might take a while to build up your mage focus, but it can be done. You're not capped or anything. Skyrim lets you do whatever.