We did a couple of cruises with the kids when they were tweens/teens - they loved them. Our favourite line is Norwegian, due to the relaxed atmosphere, no set dining times etc, but I think that any large ship that has some activities and a decent kids club would be great for tweens/teens. IMO Norwegian, Royal, Disney and MSC are particularly good for kids.
Our kids went on the slides, played mini golf, spent hours on the basketball court, played giant chess, table tennis, Wii on a giant screen, did a climbing wall, and they all loved shuffleboard! On top of stops at ports, movies, trivia quizzes, scavenger hunts, they were occupied pretty much the whole time. They never even made it to the kids club.
I'd choose the cruise by a combination of price (make sure you include everything, including drinks packages/wi-fi if wanted, and gratuities/service charges which might be added on), itinerary, and ship - for kids, it's generally the larger the better. It's also worth looking at what cabins are available - we had three kids, and NCL offered outside cabins to sleep 5, it was a bit cramped, but really not problem, and it saved quite a bit over getting two cabins. And we were hardly ever in the cabin anyway except for sleeping.