I have been on many cruises and on 4 different cruise lines. So my suggestion/recommendation to you is based on those experiences.
I think that you want your honeymoon to be special and have a really elegant setting as well as have good food, service and activities. So let me say this first. My favorite cruise line is Royal Caribbean but you cannot go wrong with Celebrity, Princess or Holland America. If you are looking for a real budget cruise and a party ship go on Carnival. If you want to basically be informal the whole cruise go on Norwegian. If you don’t mind being around senior citizens then go on Holland America. Its been my experience that Princess, Celebrity, and Royal Caribbean have the best looking ships and they are very comfortable in the cabins.
I have been on Norwegian, Royal Caribbean, Celebrity and Princess. All of these are good cruise lines. Royal Caribbean cruise line has some of the best on board activities including on various ships, ice skating or roller blading, mini-golf, table tennis, rock climbing wall, basketball court and on the new Freedom class ships, Liberty, Freedom and Independence of the Seas the flowrider where you can body surf right on ship. There are always pools and hot tubs and many ship have a Solarium (a cover area) with a pool and hot tubs for adults only. This is in addition to the regular pool and hot tubs for everyone. Some ships have water slides.
All of these lines have ships have great gymnasiums with a variety of equipment. The RC’s Freedom and Liberty have THE best gyms I have ever seen on ships.
So my advice is go on Celebrity, Princess or Royal Caribbean, pretty much in that order. And, the difference between those three and Carnival or Norwegian is kinda like the difference between a room in a Hilton Hotel vs a Best Western Motel. Both good but one definitely better.