So much to choose from - so much to see.
Hi Nicky, and Welcome to the Great American Roadtrip Forum.
Since this response is in the Field Reports, a moderator will most likely move it to the trip planning forum. But you have now seen how valuable it is to post a trip report, especially to those, who like you, come new to the forum.
The first and most important thing I suggest you do is get hold of a copy of The Milepost. It is by far the best publication on what there is to see and all the many routes at your disposal. It also includes an excellent map. A campervan is an ideal vehicle to use on this trip. There are many camping areas along the way. Be sure to check the restrictions of the routes if this is a rental vehicle.
Having driven from the lower 48 to Alaska and back three times over recent years, the last time in 2012, I have taken every route available. You could go up to Chicken and take the Top of the World highway to Dawson City and down to Whitehorse. There is an interesting side trip to the tiny settlement of Keno. Going via Tok takes you north of the Wrangler Mnts with some spectacular views, then onto the Kluane National Park.
From Anchorage you could take the Parkes Hiwy to Fairbanks, past Denali NP, or the Glenn Hwy (a spectacular drive eastbound) to Glennallan and onto Delta Jnctn and Fairbanks. Then head back to Tok and the border. Either way you are going to miss some spectacular sights or do some backtracking. But then the same goes for your drive through the Yukon, BC and AB.
There is a handy campground at the junction of the Alaska Hiwy and the Cassiar Hwy (37). At this point you have the choice of the Cassiar Hiwy and the Alaska Hwy to take you south to St George/Cache Creek, whence you will take the Sea to Sky Hwy to Vancouver and the border. I can't really suggest which is the better, as each has stunning scenery and an abundance of wildlife. That is something you will need to decide when you have The Milepost. Annually updated it is the most comprehensive publication to give you all the sights, routes and attractions along the way.
With your timeline, you have enough time to be sure to take the detour to Carcross and see the Emerald Lake and the Carcross Desert.
Best of all, you have two teenagers who no doubt can do a lot of the research of the places you will find in The Milepost. Although all my trips have been camping, either in a tent or van, I have never made reservations, preferring to just see how far I got along the way. None-the-less, if you should camp in Ft Nelson, be sure to stay at the campground at the north/western end of town. The one at the opposite end of town, is nothing more than a truck stop.
Lifey
It's a personal preference.
Nick, I have travelled in May and back in late June. In June and back in July and the first trip was in August, returning in Sept, right at the end of the season.
When you say peak season, in some ways it is, but in others it is not. By far the most traffic on the road is at the early part of the season, late May early June, when all the motor homes move up north. Then again in August early September when they all head back south again.
If you feel more comfortable with booking, you can always call a day or two ahead. But as I said, I never did. Mind you, I still never book accommodation ahead. Even though I have my van I sometimes stay in a motel or hostel, to have a change.
Lifey