I drove the Alcan back in 1989 and the roads are probably even better now than back then.
If you drive in the summer time it would be a lot better.
As far as using chains I doubt if you even need them since the colder it is the better the grip on ice is. It is always the worst around the freezing zone like 30 to 34, but if it is 10 or 20 below zero, you will find the roads not as slick.
If you are going to run chains I would probably only buy cable chains, since you can run 50 mph or so. Also if you need to buy tires for the trip, make sure to only get 8 ply steel belted radials for the gravel roads that have sharp stones that are like arrow tips.
From CA. I would run US97 all the way to the Alcan.
As far as the CB I think they run either channel 17 or 19, and it would be nice to have in case you brake down, since I'm not sure how well the cell phones work there.
Good luck.
And welcome to Truckingboards.