In the leewards/windwards, where we've mostly spent time if you watched your weather you could probably get by with one of Cam's posted Buccaneers
(kidding) but I say that because it's generally pretty easy sailing with little true windward work anyway. Generally outside the charter fleets we saw a lot of various Perry type boats (actually the Valiant 40 comes to mind at the top of his budget - maybe an Esprit 37) like the Babas, Hans Christians, on the heavy cruiser side, plenty of European models like Amiel and Ovni, Moodys and other Brit boats. We saw relatively few mainstream North American boats like C&C, Sabre, Pearson etc. But any of those should do fine as long as you keep a weather eye.
The tougher part of his plan is getting from the Bahamas/Florida area out to the windwards if that's the idea.. it's a long slog to weather getting out there and that's where I think you'll appreciate a solid boat the performs fairly well with good sea habits.
Just did an East Coast YW search with your rough parameters and the following jump out at me a bit
C&C Landfall 38
Late 80s Ericson 38 (or maybe Simon's earlier 39 - less money??)
Tartans (lots on the East Coast)
CS36T (probably my pick for this type of trip)
And not to exclude the various Beneteaus and late 80s C&Cs that might fit into that budget as satisfactory for this kind of adventure.
We sail there in a Bene 36.7 - hardly a serious ocean cruiser, but we are stricly island hopping and man, do we ever get some exhilarating rides in the gaps between islands!