You have to submit an application for permit, and you are not guaranteed the right to carry. From what I understand, the process involves putting in the application with the local police department, and they will conduct an interview of you, where they will cover: background check/criminal record, your reason for wanting to carry/own firearms, and what applicable training you have to show that you can responsibly carry/own. The ultimate decision is up to the office that interviews you. Once licensed, you are only allowed to carry/own the specific firearms and amount of ammo that is indicated on your license. You can open carry or concealed carry with a permit.
Weapons restrictions: Civilians are not allowed to possess all assault rifles, automatic and semiautomatic firearms, rifles of calibre greater than 7.62 mm or 0.30 inch, sawed-off rifles or shotguns, shotguns of barrel length 21 inches or less, rifled shotguns, handguns of calibre greater than 9mm or .38inch, armour-piercing ammunition, silencers, or extended handgun magazines.
I am told there are licensed dealers in the country where you can purchase firearms and ammo, but prices can be high. I am still trying to figure out the process of bringing firearms with me when I move. The impression is that you cannot legally own more than just a few firearms, even if you argue that you are a collector. There doesn't seem to be much solid information online on what is allowed and what isn't. I'm told that enforcement is not strict, but I would rather not risk it. I will be going to Belize sometime before December, and hope to find out more, which I will gladly pass along. I plan on staying at The Placencia Hotel, in Placencia, which has a full service gun club. Hoping to get some good info from there.
Also, I am going to share my opinion anyways
It seems there are a lot of anti-gun sentiment in Belize, but a rather sensible gun policy. I don't agree with some of the caliber restrictions, etc., but it is workable. I wish people would realize that not everyone that wants to own or carry a firearm is a "gun nut". I have been in the situation where I have needed to draw a weapon on someone to protect myself, it's not something I get excited about. Luckily, I did not have to shoot. Wildlife attacks, while also rare, do happen. I'd rather be prepared for a day that never comes than be caught unprepared.
Hope this helps.