If you have been on Disney, you know their kids program. Same with Celebrity. RCCL will be similar to Celebrity. Can't comment on NCL. But if you are happy with those lines, you will probably select from them.
Other than kids issues, Med cruises are all about itinerary, and are usually very
port intensive. "Best" is strictly a subjective personal opinion, and your opinion may differ significantly from mine. Our best ever cruise (of 15) was a 20 day Med cruise on Holland America's Noordam. Before you say Holland America is for old folks, you would be interested to know there were over 300 kids on board.
Generally, you need to think about your interests. Religion? History? Fantastic buildings? Scenic areas? Some reading on the Med Ports board, here:
would be beneficial.