If you're just coming by yourself, there's really very little other than personal effects you need to bring, other than lots of money. If you are a reader, you might bring a supply of books, as bookstores in Belize are almost non-existent and libraries are not exactly well stocked.
Unless you are setting up permanent or semi-permanent housekeeping, you can get most anything you want in San Pedro or Belize City (Belize City is cheaper for most everything, and the stores have a much broader selection.)
You can import your computer with no duty.
Belize books and publications by Lan Sluder:
Belize First Magazine http://www.belizefirst.com/
Fodor's Belize and Guatemala Guide
Belize First Guide to Mainland Belize
Adapter Kit: Belize
Fodor's UpClose Central America
Belize Book of Lists 2000