For that age range, I'd suggest any of the Royal Caribbean "Voyager" class ships, vertually someting for everyone, lots of activities, parades, ice show, etc. These ships are great for cruising with family/kids, worth looking into, best of luck.
I second that. When we go, its myself, hubby, 2 yr old son, brother and father. Theres something for each of us on board. Kids have said they really like the kids club (3+ and potty trained to use) on RCI too. Theres alternate dining facilities (Chops, Portofino, Johnny Rockets-charge a fee, Windjammer cafe (buffet), Asian fare place, room service, pizza/burger/hot dog places, ice cream stands, ben & jerry, sandwich/cafe places in the promenade which looks like a street scene with shops and parades) if you dont want the long dragged out dining room experience (though last time we had a table to ourselves and our waiters were great-getting us in and out within an hour-very important with a 2 yr old), theres the rock wall (need socks for this), inline skating, mini golf, basketball (even tournaments), ice skating (need pants and socks for this one), the arcade, pools, kids club, occasional movie, port seminars, shopping talks, bingo, card games, internet cafe (though they charge to use), library, many themed bars, disco, teens dance place, nightly shows, ice show (dont miss and get tickets early for the time you want) and probably more that I never found in a weeks time. The ships are huge, but I never really noticed the crowds, even in buffet lines. It was if I was on a smaller ship with a lot more amenities! The only extra charges are for soda, alcohol, shopping items (souvenirs, booze, jewelry, some tolietries, etc), Johnny Rockets, Ben & Jerrys (I believe), arcade games, tips, excursions, cab fares, photos taken on board if you want them, etc.
another great family cruise would be on the Caribbean Princess. Lots of daily activities and classess, lots of sports, really good kids and teen centers, "Movies Under the Stars" outdoor movie theatre. FRESHWATER POOLS that are open 24 hrs, as are the hot tubs, great service, really good food, good night life.