As to the passport requirements in Belize, you can come to Belize and live here for a year and just get a monthly stamp on your passport. Then, after the year, you can apply to be a permanent resident.
If you are going to work, you must apply for a work permit.
As to which visas are required by each country to arrive into Belize, please check the Belize Immigration department for the facts.
(Passport stamp for Belize on bottom of the left page, pictured.)