Since you're looking for lots of onboard activities - I would not recommend Radisson (even though I love it and have been on 7 times) since they don't have much on board activities and very few children on usually (might be different in Caribbean but I've only been on in Europe and Tahiti).

I probably would say that a Balcony is not an absolute necessity but make sure you get at least a full outside window cabin (might be a bad experience with small inside cabin or cabin with only portholes).