I took a cruise tour in May and found several helpful items on this web site, The most valuable were a sleep mask as it does not get 'dark' in Alaska as it does in the summer in Texas. I also found wrap around sunglasses to be very important as the winds on the ship and in Denali can be very strong and really hurt your eyes. (I purchased some ski sunglasses at Wal-Mart in Anchorage for about $10.00). Other helpful items were layers (sweaters on top of short sleeve shirts), a backpack to carry various items on day trips, a rain coat with a hood (very important), and a clock. The rooms we stayed in at Denali as well as on the ship did not have clocks, and it helps me to know what time it is - even when it's midnight and completely light outside. Another helpful tip I got was to bring an 'over the door shoe organizer.' The counter space in the bathrooms at our hotels in Denail and on the ship was very limited. By hanging up the organizer, I was able to have everything at arm's reach without having all the clutter around the sink.
As far as dress goes, I wore shorts a couple of warmer days on the ship. however, for the most part, I wore jeans at Denali and khakis on the ship. This was a much more relaxed dress code on the ship than I had anticipated - and jeans would have been fine. One additional hint - bring ear muffs and a wind breaker jacket. The wind was the toughest part to bear on colder days.
If you haven't booked a balcony cabin - I would strongly suggest it for this cruise. The public decks were jammed as we went through College Fjord, Glacier Bay, and the inside passage. By having our own balcony we were able to see everything and not be peering over the heads of others.
If you have any additional questions, please feel free to ask. This was the vacation of a lifetime, and I can hardly wait to return!