It's tough to beat Holland America in Alaska - they've been doing it longer than everyone else and have a bigger presence there. They also have some wonderful ships and great food. However, keep in mind that they do tend to attract an older demographics, so if you have tweens/teens, they may find it a bit too sedate.
If that's the case, then I would suggest looking at Princess next. Crowd is a bit younger, but they have the second biggest presence in Alaska. Food is very nice.
Celebrity, while very nice with great food, would normally be my first choice for other areas, would be next on my list because they just don't have as big a presence as the other two. They, too, do tend to attract an older crowd.
As you can see, I put in comments about food, because, like most people, we become foodies while on a cruise. And I know others will disagree with me, but in my opinion, Celebrity, Princess, and Holland America all have better food than NCL, so it becomes a no-brainer for us. Plus, as with Carnival, NCL just does not have a real big presence in Alaska.
Now, with all that said, an Alaskan cruise becomes more about the itinerary than it does about the ship because, after all, that's why you're there. So best advice is to look at the various itineraries, decide what are the most important things you want to see or places you want to go, and often this will help narrow down the multitude of choices rather quickly.
But foremost, talk to an agent, preferably a cruise specialist who's been there done that and is familiar with all the cruise lines so they can help you find the perfect cruise for you. Because what works great for someone else, may not be the best for you.