Welcome Freesail...great idea..I have a couple of recommendations which may help you get u to where u want to go..
1.) Do not buy a $500k boat right now, while u may think a cat is the way to go, after 1 or 2 years of sailing your requirements will most definitely change
2.) Buy a used $50k 27-31 ft sailboat, learn how to do the simple repairs and maintenance that always come up, get familiar with handling a smaller boat. See what u like in the boat, see what u do not like and for your next boat set it up based on your expertise.
3.) Southern Florida and the Caribbean are a great place to learn and one of the world best places to sail. Get proficient (not comfortable, PROFICIENT)with navigation, sail handling, port of entry protocol, provisioning, anchoring, sea keeping, weather interpretation and a host of other skills which you need once u slip the lines.
4.) As sailing dog mentioned a catamaran as your first boat may not be the best to learn on, I would recommend that you learn on a monohull, get your certification and then rent both thru one of the many liveries in the Caribbean, then make your decision.
Your goals are great, just go about this project as you would any business venture. Listen, learn, learn some more, go out and have fun.
Sailing is a great lifestyle, your timeline is reasonable, this website (along with others) is a great resource. Welcome aboard.
Dana Point California and the Soggy Dollar Jost Van Dyke