Over the last 51 years of driving to/from Alaska we have used most of the popular routes. The one Lonny suggests is a good one. I would decide what I wanted to see between Florida and Alaska and let that be my guide. Most trips we like to run up the mountain west area, as we often go to Colorado and head north out of there, crossing at Coutts/Sweetgrass and into Canada. We have gone up to the Boston area and crossed into Canada in New York and then west across Canada. This route will give a traveler a good taste of how big Canada is from east to west.
Our last two trips we have stayed south because of weather in the central plains. Taking Interstate 10 east to LA, pick up I 49 to Shreveport, I 20 to Dallas/Ft Worth, Hwy 287 to Amarillo, cut across to Raton NM, and then I 25 north to the border. This route is a few hundred miles farther than crossing in ND or Minn. but we prefer the mountains and avoids the heavy traffic of the upper Midwest .
Not really a bad way to go, IMHO. Lots to do on any of the different routes. I figure on about 10 driving days from south Florida to Fairbanks. Throw in a few layover days and it will normally be two to three weeks total to get there or back home. The places we want to see between Florida and the Canadian Border, we go back on other summers to visit. We try to alternate summers between Alaska and western Colorado. This summer we ran a second consecutive trip to Colordo. The route from Florida to Colorado involved going through South Dakota to Montana (Missoula area) and then south to Colorado. We are currently in the process of wandering back home from Colorado on our two month trip.
Our plan is to head back to Alaska next summer also. It is a great trip, a trip of a lifetime, that a person can do as often as they wish and all works out for them.