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Hi, Try also looking at P&O we have just been on Ventura and the kids clubs were brilliant to the point we saw little of our 3 year old - the clubs are open from 9am until midnight on a sign in sign out register, we are booking Oceana next as they also have the clubs - also they offer fantastic children prices outside school holidays whereas RCCL do not when I've looked for us. The Caribbean is your best option in January - no hurricanes and decent weather (most of the time but not guaranteed).
RCI offers the best family cruise experience by far. January you will have to go to the Caribbean though or to the Med (Brilliance of the Seas which is the best ship in the fleet IMO).