My personal favorites are #2 and #3, but I'm a weirdo. That's why I put together a few different mage builds to try. I found that by specializing, you give the game much more replayability and you'll probably have more fun. But over time I realized it wasn't how I really wanted to play, so I re-rolled. The very first character I build in Skyrim was going to be a generalist. And no - just because you're roleplaying doesn't mean you need to speak like you just stepped out of Medieval Times.
This allows you to focus on just a few schools and roleplay more. You invest points in every single school and enchanting, making you a jack-of-all-trades but a master of none. The way I see it, there are two main ways to play mages in Skyrim: because you are going to play as a mage, right?