Sit down at the police station and be patient and polite, they will explain the rules to You. Permits come out of Belmopan and ammunition is also with a permit. You can shop for the weapon in Belize city, pick it out and then apply for that specific firearm while the merchant holds it.
Expect an interview and a document stating you have no police record, ironically the document is called 'Police Record' you can apply for a police record at the police station with $12.bz and two photographs.There is a yearly fee as well.
Don't know anything about importing a weapon...bet it's much harder.http://icbl.bz/lob/Chapter%20143S.pdf