A few pointers. Universal weather is a good place to start. They can get you the eAPIS, file your flightplan, get you the cuban overflight, custom forms and immigration forms, enroute charge reports, arrange discount fuel from the local fuel vendors and help you with the ground handling at both KIN and MBJ. Highly recommend you use them at least a couple of times before you try doing it on your own. Ask them about the overflight waiver so you don't have to stop in florida on the way back from Jamaica, they should be able to help you out with that. One good thing about UV is that you can make all the payments directly to them.
Both KIN & MBJ have reasonable landing and parking fees. Fuel is cheap about $2.80 per gal. They'll charge you for ATC services rendered in the terminal area, passenger fees, passenger security fees and navigation fees. When you get there, take a bunch of immigration and customs forms back with you so you won't need to get them from UV the next time you're heading that way. If you need to refuel, take fuel immediately after landing so you won't have to wait for the fuel truck on your way out, the fuel guys will fuel the big guys before they head your way.
Did i mention use UVair... Oh you could use Jepp too. Make sure you got locks for your plane if you're sending the night.
Lastly try the jerk pork, curry goat, fried & steamed fish and anything else Jamaican you can find.
Enjoy your trip. If you need anything else just let me know.