As far as fishin' line goes, what you have on your rods and reels will prolly work... but!... given the clarity of the Carribean waters, you will catch alot more fish with a flurocarbon leader 4 ft. at least, and the longer the better.
I love to target the Snapper (Muttons and Lane), very tasty! Bounce bottom with a 6-30' (I'm not exagerating, a 30' leader!) leader and a frozen Sardine or live Pin Fish in about 100FOW and hang on! ?The thing I love most about saltwater fishin' is, you never know what you're gonna pull up... could be a Grouper!... could be a Shark!... cou;ld be a Snapper!.. or it might even be a Snook! (which are also very good eating!)... but like CH said, check the regs before you keep anything.