I've taught in Belize a couple weeks every other year since 1993. A couple thoughts:
1. Atolls are better than other sites. Glovers Reef is cool.
2. The Blue Hole is a geologists dream, and as a seaweed guy with a light the last time I dove there I got a little excited. However, aside from the sharks it's not much in terms of animals. That said, most dive trips out there combine with a couple of really nice, diverse wall dives on the outside of Lighthouse.
3. Never been on a liveaboard, and the idea appeals to me, but as somebody "day tripping" I can't say I'm a fan of being where the liveaboards are. Having a small group diving and then suddenly having 30 people in vaguely organized masses dropping down on top of you turned me off a bit. But as I said, I'd love to be one of the 30! If you can afford it, I'd try to visit some sites in the south, AWAY from Ambergris/Caye Caulker and even Lighthouse. There's a lot to be said to be where others are not.
4. Time of year is fine.
5. Having been there pre- and post- hurricanes (long stretch with no hurricanes until about 1998, then 3 hurricanes in 4 years) and seen bleaching/recovery, I think there's room for multiple perspectives. The coral is a shambles after a major hurricane like Mitch, and nobody likes to look at bleached/dead coral. On the other hand, if all is going well for the corals it's pretty nice.
Enjoy!