We have taken 4 cruises -3 with Carnival. We tried out Norwegian, but returned to Carnival because we had a better experience. In my opinion, they are a GREAT value. I have always thought the food was very good, that there is always something fun to do on the ship, and that the service is excellent. We haven't gone since our son was born, so I can't speak to any of the kids' activities, though it seems like there is always a lot for them to do.
I would assume that the fancier cruiselines would be nicer, but I have had no problems with Carnival. We have cruised on the Celebration, Elation, and one other, but I don't remember which. We have done shorter trips (4 or 5 nights), and have gone to Cozumel, Playa del Carmen, and Cancun. They always have a ton of excursions to choose from, though now that we have been a couple times, we have started booking our own when we dock, since it is cheaper.
I think you will all have a good time on Carnival. Though I don't see how one could have a bad time on any cruise! We will defintiely be cruising again once our kids get a bit older.