Visa & Master are widely but not universally accepted. Others are risky. Using a CC your bargaining options are limited, as they cost a lot for the merchant. The ideal is to bring some US cash (always accepted), some low-denomination US$ travellers' cheques, and credit cards for emergencies. Also a debit card if you need to draw cash. Tropic & Maya take cards, though Maya often gives substantial discounts (up to 30%) if you give them cash.
Belize is not a credit card society, though they are often accepted. If you want to use one check before you incur a bill, as if you can't pay by another means you will be in the wrong, not the merchant.