Scott,
My wife and I have spent about two months on CC in the past year. 9during three visits ranging from about two weeks to a month. CC is friendly and very laid back. Don't expect anything to happen quickly, although sometimes it does. You will need a bike to get to more remote areas of the island, but if yo stay in town everything is close and in walking distance. Our daily routine usually consisted of a leisurly breakfast at home, then a bike ride perhaps stopping for some groceries (usually a a daily grocery run). During the afternoons we would frequent the split where you can have a snack and drink belekin all afternoon for about $20 US.
A lot of time was spent stopping and talking with folks we had befriended, you will see people often. We usually cooked dinner at home.
We spent $750 US a month for a furnished 1BR apartment. Our apartment was comfortable and had a small kitchen with hotplate, microwave and some utensils. Prices vary widely with location and amenities. You can get a place for as little as $300 US a month, but is is an unfurnished shack and likely has a shared latrine. Ask questions about utilities, water quality (I suggest town water), wifi, or whatever else you will need.
We made a trip to Belize City to get a few household goods and see what that was like. We bought everything else on the island including our bikes.
Aside from our rent the bikes and some minor home goods we spent around $1,000 US for living expenses water taxi, and entertainment etc.. It might be a good idea to volunteer to do something for a school, church, or the humane society...whatever. That will give you the opportunity to get to know some of the residents. We were invited to dinner many times because of our activities on the island.
Most importantly remember to be friendly. Don't expect things to be like they are at home and enjoy the opportunities presented to you!
Ambergris Caye 
AmbergrisCaye.com