Check Hyde. Some places will pick up at your front door and deliver to your front door here in Belize. Other places will do port to port shipping so getting it to/from the port will need extra arrangements. There are a lot of options out there so search around. If you're moving down, you could always cruise down and get off the ship in Belize City. If you're just looking to ship clothes and books you might be able to fit this all in a few suitcases. Cruise ships have higher luggage weight requirements than planes. The downside, it's only one way. Just my .02
You can do USPS, FedEx, or DHL. USPS would probably be your cheapest route. Even if you have a friend who works for FedEx and can find someone to give you a 75% discount, it's still very expensive. And yes I live in San Pedro.