Welcome to Cruise-Chat. You have several good choices for a multi-generational cruise.
Tops on the list for younger passengers (the 3 20 somethings) would have to be Either Carnival (but they have only one ship doing Alaska on one way voyages only) or Royal Caribbean (more choices and they do both one way or round trip). Alaska is not much of a party destination and even these ships will have a good mix of age groups. The NCL Pearl is another very good choice for a lot to offer for each age group and plenty of younger passengers as well.
The other lines will have a little older avg age and not a lot of 20 somethings. Princess would be another good choice they, along with Holland America will have more ships and itinerary options than anyone else there. Scratch Holland from your list though, it would not be a good choice with a mix of younger passengers. That just leaves Celebrity and some lesser known options I won't even go into. I'd also scratch Celebrity with 3 20 somethings.
With your demographics I'd say a good list to look further into would be, in no particular order....
RCCL Rhapsody of the Seas
Norwegian Pearl (Probably the nicest ship there although a little different experience from the more traditional cruiselines.)
RCCL Serenade of the Seas
Look at who has the best values and itineries you prefer. I'm sure there will be others here with alternative recommendations as well. Have a great time and let us know what you decide.