Most stony corals you will find while diving the keys are protected I think. You could go with Zoanthids, Palythoas, photosynthetic gorgonians, rock anemones, condylactis anemones, etc.
+1 All stony corals in the Atlantic are protected.
The Palythoa found in the Caribbean are pretty ugly IMO also contain some of the highest concentrations of Palyotoxin out of all them.
Gorgs will be the coral of choice for get that Caribbean reef look, good thing is the photosynthetic ones are not only easy, they are pretty cheap too. Briareum asbestinum, pseudoplexaura are common to see in the trade, look for gorgs that have brown polyps, brown polyps=zooxanthelle present (could be exceptions, but this is the general rule.)
I would avoid the iconic Caribbean sea fan Gorgonia ventilina, despite being photosynthetic as it can be rather difficult as its Flow demands rival that of Acropora. Plus rare to see these days in the hobby, they might be protected now as well possibly.
Like others said add Caribbean fish, maybe a coral banded shrimp a condy nem or a nice S. helianthus nem (bit trickier) and you are rocking.
Love Caribbean biotopes, definitely throw up some pics as you make progress