We used our Bank of Montreal debit card at Belize Bank both in Belize City and San Pedro.
On the advice of our hosts, we brought Belize cash and US dollar travellers cheques to use in San Ignatio and Benque Viejo del Carmen. We didn't need to use the travellers cheques so I don't know how or if they are accepted on the mainland. They were accepted everywhere we shopped/ate/drank in Belize City and on Ambergris Caye.
We used our credit card sparingly for larger purchases as it seemed that most businesses charged a fee for processing.
So all that said, a combination of all three with a few dollars in US cash for when you arrive, and you should be all set to spend every cent you have