I've never done an Alaskan cruise, so I can't speak to that, but I've been on two Norweigan lines trips through the Caribbean, and both were spectacular. If, as you say, you're into warmer cruising, then a Caribbean cruise is definitely a good way to get your bearings as to the industry.
Eastern Caribbean is going to be more beaches and islands (usually Florida Keys, Bahamas, Virgin Islands, etc.), while Western Caribbean will likely highlight Jamaica and Mexico, which would give you a chance for shore excursions to see things like Mayan ruins.
Depending on your interests your preference may vary, but if I had it to do again, I'd definitely choose the Western Caribbean routes.
For something more adventurous, cruises throughout South American ports, the Mediterranean, and even to Antarctica are said to be tremendous.
Hope you find what you're looking for!