Silk's advice is right on.
I always take $200-500 cash with me, in smaller denominations, and a wad of $1s for tipping porters and such. I also take the rest of my "fun money" funds in traveler's cheques, some in $20, $50 and $100 denominations. If you take it all in $20s, that's one big wad of paper.
However, as Silk said having the $20 are easier to change at the little stores. I can always get the bigger ones changed at the hotel, dive shop, etc. (Worst case scenario, you can get it changed at the bank or the Western Express).
I only use my credit card for my acco and/or diving and only then if I've used up all of my traveler's cheques. That said, I've never had a bad surprise at the exchange on my VISA bill when the charges finally shows up back in Canada. Therefore, charge conversions should be even cleaner for Americans.
I prefer to use cash for drinks and dinner, especially if having a few drinks. It's easier to pay as you go and then there is not as much chance of a misunderstanding over the number of beverages consumed as the evening wears on, if ya know what I mean.
You start out using American dollars and you'll get your change back in Belizean currency. So, for example, if you purchased something for $16.00 Belizean and gave a $20 U.S. bill, you will receive $34 BZ in change. If you purchase something for $16 U.S. and tender a $20 U.S. bill you will receive $8.00 BZ, in change. On occasion, you'll get a mixture, and for the last example, you might receive $1 U.S. and $6.00 BZ in change.