Norwegian Cruise Lines and Royal Caribbean Cruise Lines both would be good choices for your age bracket. The both have ships leaving out of Seattle; the Norwegian Jewel and the Rhapsody of the Seas respectively. The ideal trip to Alaska would be to do a seven day cruise and also add land time, pre or post cruise to see Denali National Park and other others inland. If you only have the typical seven day vacation then going roundtrip out of Seattle would probably be best for airfare. You can also do a one way start in Anchorage (Seward or Whittier) and sail to Vancouver, or vice versa. Leaving out of Seattle a typical cruise would be to stop at the big three ports of Ketchichan, Juneau, and Skagway, with a day at one of the glacier which you don't leave the ship. You also would stop at Victoria, Canada to meet the foreign port requirement.
I've been to Alaska in both of the months of August and September. The weather can be finicky so you want to prepare for anything. Dress in layers.
I would highly recommend you find a travel agent that specializes in cruises and can go over the differences in the cruise lines and match you up with the one that meets your expectations.