My two cents worth:
I've seen nearly all the properties on Ambergris Caye, stayed a quite a few of them (including SunBreeze and Banana Beach mentioned here) and agree that all the ones mentioned are nice and could be good choices for you.
I was really impressed by Banana Beach -- beautiful one-bedroom suites, nice pool, on/near very good beach, efficient and friendly management. But then I like SunBreeze for its great location and shady pool ... and most of the units at Paradise Villas at the north end of town are nice, too.
There are a number of other fine condos and hotels south of town that would likely fill the bill for you, including (only those with pools listed)...
The Palms, Belize Yacht Club, Villas at Banyan Bay (if you want a two-bedroom unit), Tropica, Sunset Beach and Caribe Island.
This doesn't include some of the good places on North Ambergris, which is a little more away from things.
Belize First Magazine http://www.turq.com/belizefirst/