There are no charges for Camp Carnival, although I'm sure they'd appreciate a tip at the end of the cruise.
My wife and daughter did Disney last year, and we've all done several Carnivals, Princess, and HALs. Disney probably has the best kids activities, but my kids like Carnival and Princess fine too. I think the Disney stuff has more hands on activities that parents are supposed to participate in.
No worries, they'll love it!