I have to agree with hydster. We've cruised on many different lines including NCL,
Royal Caribbean, Premier Big Red Boat (now defunct), Princess and Carnival several times. We were most recently on the Carnival Inspiration over Thanksgiving, and never saw a single drunk. The passengers were made up of about 1/3 families, 1/3 older couples and 1/3 singles/young couples. The Inspiration was built in 1997, so it was one of their older ships but it was in great condition. They have LOTS of newer ships, but even the older ones are pretty nice. We never saw any drunks on NCL,
RCCL or Princess either. I have heard that the 3-day Carnival cruises do tend to get a younger, more "partier" crowd though, probably because they are cheaper. On a 7-day, they should be fine.
I wholeheartedly agree with checking cruisecritic.com and going to the board specific to the line you want to cruise. There are a lot of fun people on the Carnival boards who are very helpful. The best tip I ever learned is to book your excursions on your own. We've done this the last few times and saved a ton of money, plus the excursions were nowhere near as crowded as the ship-sponsored ones.
I've been to just about every Caribbean island at some point except for Aruba and Roatan, so if I can answer any questions at all, please let me know. I can say that my least favorites are Jamaica, Nassau (unless you go to Paradise Island) and Belize. My favorites are St. John, St. Croix, Bermuda, Grand Cayman and Cozumel, all for very different reasons.
Please let me know if you have any questions, I'd be happy to help.