Think DRY, WARM, COMFORTABLE, and LIGHTWEIGHT for your boots and basically most of your gear. 

Like Rogie posted, your boots should fit well, be designed for long mountain walking, and be WELL BROKEN IN.  I used a pair of hard, climbing style boots that I had worn for years on one Bighorn sheep hunt, and I had blisters on top of blisters.   I finished the hunt in tennis shoes, and the boots went into the trash when I got home.

Lightweight tennis shoes for around camp and for crossing creeks (keeping your boots dry) is also a good idea.

A lightweight and waterproof rain jacket and pants are a must.  They should be large enough to easily fit over your other cloths.  Also a small 6'x8' plastic tarp in your daypack can make a quick, dry shelter when an afternoon rainstorm catches you with nothing but dwarf willows to hide under.

On the second leg of my Canadian Dall sheep hunt, another hunter in camp loaned me a Therm a Rest sleeping pad.  It was MUCH more comfortable than the air matress that I brought.

A small gun cleaning kit with oil can save your rifle when it gets wet.

Also on my Canadian Dall Sheep hunt, heavy rain kept us in the tent all one day, and my guide and I each read books that we each brought, then we switched and read the books the other brought.

Alaska law requires you to bring out all edible game meat.  My guide and I carried out my ram and our camp.  You'll need a strong, but lightweight backpack and frame.

Have a great hunt.