If you go with a satellite connection, you are likely to need a 7' dish as this place is at the edge of the satellite coverage (probably depending on which provider you subscribe to, though).
A Starband connection works really well with a 7' dish and brings 700-800 kbps download speed and very few drop-outs, which is very good (for Belize) and more than sufficient for most things (Internet TV and radio, music downloads etc.), at a monthly cost of approx USD 150.00 incl. their "small office package".
My experience is that all US based services require a US address and social security number, so this might not be for everyone.
Julian at the computer store in Middle Street (by Martha's Hotel) is a good local business to talk to about this.