I know nothing about agriculture in the Caribbean, but I would suggest taking advantage of the local produce and starting there.

Do you have any ideas on what you want to grow?

I checked the Caribbean Agriculture Agricultural Research and Development's website (www.cardi.org) for some information. They have annual reports, that stop at 2011 for some reason. I would read some of them to get an idea of what are the current trends.

One idea that comes to mind after reading the 2011 report is producing high quality seeds. Grain prices for direct consumption are not as interesting.

I would also search for local farming associations to get to know what people are doing.

I suspect that the Caribbean will be more susceptible to climate change than other regions, so food security might become very important in a near future.

Good luck!