Celebrity, Princess, Holland America, Regent Seven Seas.
Those would be my choices and in that order. Concentrate on cruises that are when school is in session. Cruises that are longer than seven days, tend to have the fewest children.
Holland America, can and probably will be, a bit older but it is enjoyable and Regent Seven Seas will be the most expensive but it is the most "all inclusive" and have the largest standard cabins.