Toodles, you need to check out the BTB. Belize Tourism Board as a start. http://www.belizetourism.org/
Another good resource is Toucan Trail. http://www.toucantrail.com/Home/
Moving Guide to Belizehttp://www.movingtobelizeguide.com/
Passports and Visas are issued from your home country. Assuming you are coming from the US, you should do a web search for recommendations about innoculations. Nothing is required at this time, but malaria prophylaxis is something to think about if you are in a jungle area.
At age 19, you will need to obtain permanent residency status in order to be allowed to work. That means you will need to have enough money to live on duriing the year or so waiting period.
Start doing web searches and you will find answers to all your questions.
I've been doing that for months and months and months, reading these forums, researching, planning, budgeting, etc. Although my circumstances are different than yours, it does not appear to me that living on $500 a month would be an easy thing for a 19 y/o from the US to adjust to. That would be a very spartan lifestyle. Belize is a developing country. Basic things such as electric, phone, gas, etc is equal to or more expensive than in the US. Clothing and food as well. Food being more expensive if you expect to eat and drink things you are used to. Think about this: Cornflakes = ~$8.50 a box.
Good luck to you. Don't give up your dream. Anything is possible when you put you heart and soul into it.
I'm counting of the residents and frequent posters on the forums to correct any information that I've provided that may be inaccurate.