This question is harder to answer than you think. There are a myriad of choices of ships and cruise lines for Alaska. Princess, HAL, Celebrity, Carnival, Royal Caribbean, NCL and others have Alaskan cruises.
Do you want to leave from Seattle, Vancouver or Anchorage. Do you want to return to the same port or go one way?
One way cruises give you the opportunity to explore after the cruise. This could be Vancouver or "near" Anchorage. Only smaller ships stop in Anchorage. The cruise ships stop in Seward or Whittier which are about two hours south of Anchorage. The drive from Seward to Anchorage is beautiful.
My first choice, for a first time Alaska cruise, would be a round trip from Vancouver. You will be able to cruise the Inside Passage and see some gorgeous scenery. I would also suggest choosing a ship that goes to Glacier Bay. This rules out Celebrity or Royal Caribbean. They do not go into Glacier Bay but do go to Tracy Arm and Hubbard Glacier, which are beautiful but, in my opinion, not as spectacular as Glacier Bay.
From your description, I would look at Princess or HAL. Specifically the Coral Princess and Volendam. They are beautiful ships but do not have the "glitz" of a Royal Caribbean or Carnival ship. IMO: Princess and HAL do Alaska the best with on board lectures, naturalists and Officers of the National Parks Service. (Other cruise lines also have Officers of the National Parks Service when going through Glacier Bay.)
Another option is: Norwegian Sun. It is a Freestyle ship and if you are use to traditional dining then this may not be for you. I personally love NCL.
If the Voyager Class ships are what you like then you may want to Carnival Miracle out of Seattle. That would probably be the closest in decor to a Voyager Class ship. The only negative about Seattle is that you go west of Victoria Island and bypass the best of the Inside Passage.
I hope you can find the cruise and ship that's right for you.