Chloroquine has been used for decades (I had to take it in Vietnam, which was, what?, three or four wars ago.) It has few if any side effects. I've taken it many times with zero side effects, and in fact I'm taking a version of it now (unrelated to malaria.)
But if you are just staying on Ambergris Caye and making a trip or two to the mainland, there's really no need to take malaria prophylaxis, despite what you read on the CDC Web site. The CDC is very conservative. I'd say 98% of visitors to San Pedro don't take anything.
There is malaria in Belize, but in recent years the number of cases has been very small -- a few hundred cases annually, mostly among immigrants from Guatemala and in remote areas of the far south and west. It can happen, and I know of a few visitors who have contracted it, but it's rare. You're probably more likely to die in a traffic accident or to have a heart attack while snorkeling than to get malaria.