WHAT SIZE MOTORCYCLE?
A common misconception is that you better ride a big bike, 1000 cc or bigger. The truth is you can ride any motorcycle, even a small scooter. Any and all sorts of motorcycles must have been ridden to Alaska. It is totally ok to go with medium size motorcycles such as 650 cc. Lousie on the Loose is a cool and inspiring book that details how a girl from UK rode air cooled single cylinder, Yamaha XT225(formerly known as serow, 225cc engine) with tons of camping gear, tools and some spare parts all the way from Alaska to Patagonia. That should testify that even small size bikes can make the trip to Alaska. It depends on your budget and how quick you want to complete the trip. If you are in a hurry, yes a bigger bike will eat more miles in a given time. But if you have a month to do a round trip, you can do it with smaller motorcycles.
WHAT TYPE OF MOTORCYCLE?
The road conditions have improved a lot over the years. Even sport bikes can do the trip. But the slippery wood and metal bridges can make you wish you had a dual purpose/enduro type of bikes while crossing countless rivers on the way to Alaska. Also the fact that there are a lot of construction and maintenance work on many sections of the road makes dual purpose bikes with some off road worthy tires a vise decision.