You should think hard about the Caribbean requirement. Most any coastal cruiser can make it across to the Bahamas if they wait a few days (sometimes weeks) for a weather window. But unless you want to spend a month or better getting past Puerto Rico by doing the "thorny path" (see Van Sant reference below it is harbor hopping while waiting for nice weather windows each time), then you need as they say "a bigger boat".
Well bigger isn't really the criteria. Tankage is one, but many coastal cruisers can handle the longest leg to
PR. Superstructure strength (scantlings to use the NA term) that can take multiple slugs of green water over the bow and into the front windows without tearing them up. Sure you can wait for weather but you might find yourself sitting in many harbors along the DR coast for a while to get the right conditions.
Boats like the Nordhavn, Kady Krogen, some Selenes can do it. Nordhavns also have redundant or very robust systems to keep you going in rough offshore weather.
Stabilizers is more a comfort thing than a safety one, but many won't go there without it.
So think about the Caribbean requirement. There are lots and lots of lovely places to go in the Bahamas that don't require that kind of boat.
If you are serious about the Caribbean, get yourself a copy of Van Sant's A Gentlemen's Guide to Cruising South.
David