Getting the license is cheap. Hit
the ARRL Website for a test area near you. You can pick up any of a bunch of study books. (Radio Shack had a good one when I was studing) and you take two (Novice and Tech) to get your basic no-code license.
Now the problem is that getting to the Caribean from here on the 50 Mhz or greater that the no-code license allows is tough.
For world wide or AM skip type ability, you still need to take a code exam. There are all kinds of tapes and PC software that can get you ready for the code. It isn't hard, but you have to make the effort. IF you have a good ear for music, it helps. Basically, you are going to train to hear patterns. You only need 6 words a minute, but I've heard that it is actually easier to train using a cadence of 20 words a minute with long enough pauses to make the actual count only 6 words a minute as it makes the patterns easier to hear.
Ham Radio Outlet in Salem NH or online is a great source for equipmnet. I also like local swap meets if you know what you want as the prices are great.
Now you can go absolutely crazy with equipment, but even cheap equipment will work great if you spend the time to set up a good antenna. My first 'base' radio was a little walkie talkie with a 30 watt amp. However, I had a well tuned cable and antenna so that 30 watts could carry a LONG distance. Total cost was about $500 by getting the basic equipment and power supply at a swap meet and then spending the time rigging the antenna.
Don't go thinking you need the latest computerized radios. Older designs work as well. Put your $$ and time in a good antenna.
You should also ask around to see what kind of bands are working well into the Carribean from New England. That will help you decide on what frequency you will need to use. The lower the frequency, the larger the antenna you will need. A lot of the theory and such will be a part of the study, so don't sweat it.
If you have a good mind for science or math, the basic concepts are not going to be hard at all.