Juneau and other ports in Southeast Alaska are in the heart of the Tongass Natinal Rainforest. It is very likely that you will experience rain at one point or another during your trip so I would bring a rain jacket.
It is a remarkable experience to walk on a glacier but it is good to be dressed for the occasion. The tempetature on the glacier may cooler than the temperature on land so you should bring a jacket and dress in layers. More than likely you will not need a hat and gloves but it never hurts to bring them along.
The are many activities at the Mendenhall Glacier Visitor Center. East Glacier trail starts right behind the visitor center so you can literally start hiking a couple minutes after your arrival. Explore flora and fauna on a nature trial or observe wildlife from one of the many viewing platforms. Since this is a national park the gronds are very well maintained and many areas are wheelchair accessible. There is a small fee to enter the visitor center.