First, you'll want to talk to a Cruise Specialist who has been there done that. Do not book directly with the cruise line.
Also, one-way cruises either northbound or southbound will start or finish in Vancouver not Seattle, so take that into consideration as it will affect your airfare.
There are some really good cruise tours being offered and for most people those work best over doing your own tour and then doing a cruise. The cruise lines will take very good care of you during the tour part of your cruise tour and while they are a bit more expensive than doing your own thing, some people find it reassuring to have everything taken care of for them.
But Alaska is awesome and definitely some place you will absolutely love seeing! We thoroughly enjoyed our 2 weeks on a cruise tour and can't wait to go back. It's a magical place, the people are awesome, the food is great, and the experience is awesome!
With that in mind, Holland America has been doing Alaska longer than any other cruise line and have more ships there than anyone else. However, they do tend to attract an older more sedate crowd, so they may not be what you're looking for. Second on my list would be Princess, followed by Celebrity.
Again, it's important to talk with someone who knows all about it and can help you work within your budget, timeframe, and itinerary.