We are in the same situation as you - kids aged 11 and 13, planning our first ever cruise during the April half term holiday. We have done loads of homework over the past few months (takes us ages to book anything), and the line that keeps getting recommended to us is Royal Caribbean.
Apparently the kids activities are superb, a work colleague showed me a daily programme from her cruise and the kids had loads of things to choose from, they were even making mini volcanoes and exploding them

I am told that their teens programme is also very good.
Our kids have gone through all the brochures with us and are awestruck with the fact that if we go with Royal Caribbean they could ice skate, surf and climb walls whilst at sea! Let your kids have a look at the brochures - they might choose for you