I think reviews of Carnival as the "party ship" are grossly over-rated.
I think you will find times of year, when you get more partiers on every line (spring break and other school breaks for example).
When DH and I cruise by ourselves, we tend to prefer RC. From our experience, you will get mostly people in the 30s and 40s. This too depends on time of year. In the summer and early fall, you wil get lots of honeymooners.
When we cruise with our kiddies (3 and 4) we will cruise with Carnival because they offer the best price deals for families. I refese to pay normal 3/4 pax rates with RC for my little guys. Perhaps when they are older.
We are cruising next March on HAL. I got an amazing deal with the kids for $99 plus port charges.
We've cruised Princess before and found the crowd to be too old for our taste. I think you would do well on RC or Celebrity. Has anyone cruised MSC, I'm just hearing about them now.