I agree with the other posters as to which cruise lines. My personal preference would be Carnival for younger people, but Princess is also great, and HAL was super to us on our honeymoon, but we were in our 50's at the time.
You might also want to research your itinerary with the number of ports in mind. Some cruises are port-intensive, while others have more sea days (more quiet time to relax as well) If you're looking to visit a lot of island to choose one for future vacations, then choose a cruise with a lot of port stops. One of my favouite itineraries is one that include St. Thomas, St. Maarten, Aruba, St. Kitts, St. Lucia, and Barbados. All lovely islands to visit.
Good luck, and happy honeymoon!