Something like a westsail in the 40 foot range, Good safety stuff., Life raft etc. People are going to try and talk you out of it, don't listen, stay focused. Come down to Miami and charter a boat from fla. Yacht charters and sail around on it with a blue water captain for a long weekend and get your feet wet. Then go from there.
I agree with Capt. Aaron to not give up on this. Just be aware it is a trip that takes a lot of planning and preparation.
Chartering a boat for 3-4 days with an experienced captain is a good idea and a good start, just make sure those 3-4 days includes some ugly weather so you have some idea of what to expect when you are in the middle of the ocean and it turns ugly on you...and it will.
I've got a couple of friends who crewed on a boat at our marina bringing it back from the Caribbean to the Chesapeake Bay via Bermuda. The first leg was fairly quiet and uneventful. The leg from Bermuda to VA was not. They had to heave to and ride out a storm for 36 hours. It was not fun.