I think Carnival's reputation is to have more of that "party" atmosphere that you like than other cruise lines. Royal Caribbean and Princess are pretty similar to each other, and you may want to check Norwegian Cruise Line as well.
The atmosphere in general on Europe cruises is a little different than Caribbean cruises. There are so many stops in different ports, that you'll probably be spending more time off the ship on a European cruise than an eastern or western Caribbean cruise.
As for beaches, if the ports are anywhere near a beach, there will be excursions to that beach or beaches offered by the cruise line. Just check the geography of the places in which you're interested, to see if they're near water or are landlocked.