Celebrity or Princess. check out the reviews of previous travellers on cruise critic for an honest opinion.
I've never done Alaska but have heard that Princess are excellent in this are.
I have sailed on most of the lines and would highly recommend RCI (Royal Caribbean International) - forget Princess, P&O or Holland & America as they are all now owned by Carnival and have the same policy on all there ships - "£Bleed the passengers dry and cut all the good bits". RCI too are trying to be "Competitive" with prices and you have to be vary of waiters offering a welcome aboard drink in a special glass. After offering you a cocktail and you start to drink it they will ask you to sign a slip and charge your stateroom with $##. The main difference with RCI and the others is that they tend to offer the best shore trips at sensible prices and on Alaska cruises the trips are spectacular. If you like helicopters then a must do is to land on a glacier and walk a while. Even gentle white river rafting is possible though you might get wet. I would recommend an aft balcony cabin (over the engine screws) fantastic views.
We've been cruising for nearly 20yrs[now both in our early 50's]and our favourite cruise line is Holland America. We have been on 3 Alaskan cruises with them and have not been disappointed. Their fleet are 4/5* and quite reasonably priced.The main bulk of the passengers are American which suits us. We had pre booked premium suites on 2 cruises and had a last min.'bowels of the ship'cabin on the third.Suites are a marvelous way of traveling but on an Alaskan cruise where you are out on deck[often in cool/wet weather gear]watching and absorbing the amazing scenery,it really does not detract from the holiday to be in a much lower down cabin especially if it's a cheap last min. bargain like the one we had.Go for it, it's one of the 'must do' cruises.