Most direct and most economical are usually different.
Most direct is likely American Airlines nonstop from Miami (MIA) to Belize International (BZE) and then either Tropic Air or Maya Island Air from BZE nonstop to San Pedro (SPR).
Most economical would vary depending on when you are going and probably how far ahead you are buying your international ticket. Some people find that the cheapest route is flying to Cancun, Mexico (CUN) and taking an ADO bus to Chetumal, Mexico, and then either a water taxi direct to San Pedro, or alternatively a bus from Chetumal to Belize City and then a water taxi to San Pedro ... or an overnight ADO bus from Cancun to Belize City and then a water taxi to San Pedro. But this would vary a lot depending on when you go, and recently flights to Cancun have been getting more expensive.
Kayak.com or one of the other metasites that compare airfares on major airlines are usually a good way to find the best deals.
It might even be that a Greyhound bus from Miami to the Mexico border at Brownsville, Texas, and then a bus through Mexico to Belize would be cheapest, at least if you didn't eat much and slept on the bus, but it would be a long (like 4 days or longer) and very hard -- but possibly memorable -- trip!