My favorite cruise line is Carnival. Good service, great food, nice clean ships, bigger staterooms, younger crowd, and lots of activities. Plus, I get a $100 on-board credit for being a stockholder. I especially like the Conquest Class ships (950+ feet long, including Freedom, Conquest, Valor, Glory, and probably another ship I'm not thinking of).
Royal caribbean is nice. Bigger ships (much bigger in some cases), decent service, good food, and medium age crowd (some young, some old).
Norwegian is a good line. Ships are comparable to Carnival, except perhaps slightly more polished. The staterooms are generally smaller, the crowd is about like on Royal Caribbean, and there are some activities. The food on Norwegian is excellent, but only if you eat in the extra-cost "specialty" restaurants. The food in the included no-extra-cost dining room and buffet is ok (think general chain-buffet quality, things like meatloaf for lunch, and things like chicken parmesan for dinner), and much less tasty than on Carnival in my opinion.
Those are the three lines I have been on recently, including several cruises from Carnival and Norwegian. Again, my favorite is Carnival, which provides a great cruise experience, usually at the most reasonable price, and I don't feel like Carnival is constantly trying to nickel-and-dime, as I do on the other two lines.
If it is a Caribbean cruise you are looking for, you will probably need to be thinking whether to do "Eastern" or "Western" Caribbean (if you plan to cruise out of Florida). Eastern will have ports like St. Thomas, Nassau, Bahamas, Key West, St. Martin/St. Maarten or Grand Turk. Western itineraries will include ports such as Cozumel, Mexico, Costa Maya, Mexico, Grand Cayman, Belize, and Jamaica. Of those, my favorite ports are St. Thomas USVI, Nassau, Bahamas, Grand Cayman, and Jamaica.
I've been to most of the islands and ports by now, but if you are new to Caribbean cruising and between 20 and 45, I would probably book a 7-day on Carnival, and pick the lowest price on at least a Conquest-class size ship (cheapest will probably be Western, and I recommend making sure Grand Cayman and/or Jamaica are on the list of ports of call). For a nice 7-day departing August 29th, 2010, expect to spend $399-$479 (including port fees, but plus tax) per person for a 7-day semi-inclusive cruise (includes meals, and most activities, but not alcohol, soft drinks, tips, and shore excursions) in an inside cabin if you book early. Since it is your honeymoon, you may want to book a somewhat nicer, bigger room with a balcony. Balcony rooms start as low as $559 per person to around $759 per person if you book early enough (I would probably recommend the bigger balcony room for a honeymoon).
If you get seasick, book a midship cabin, on a lower or middle deck. You do not want to be up top at the front or at the back of the ship if motion bothers you.
I hope this is of some help, and congrats on the upcoming wedding!
Yes, I do cruise a lot.