If you just want to "go boating in the caribbean", fly to BVI and rent something. I've rented and taken some center consoles from Tortola to Peters Island, Jost Van Dyke, etc. Waters are pretty forgiving, for the most part, you generally have line of sight between islands, and other boaters are pretty helpful.
You can also rent some nice bareboat or crewed cat's out of Road Harbor marina, among other places, if you want to do some extended trips.
If you want to take your own boat down there, presumably from FL, then you'll want to spend a little more time getting used to your boat, and the waters. There are always people going back and forth, so some buddy boat trips on your first couple of crossings would be recommended. Start with some runs to the Bahamas, figure out max seas you (and/or your boat) can safely handle, ensure you have plenty of safety gear and a full tank of gas
