These guys
Clickyare the biggest renters. Mostly class Cs but they are kept in good shape.
Campgrounds in the northeast tend to fill up on weekends starting late June, but you should be able to find a spot without advanced reservations. I would set a general route and look at stopping every 300 miles for a couple of days. When you're at campground #1, you should have reservations at #2 and be looking for #3. The only reservations I'd make now would be July 4th and it may already be too late.
I'd skip Canada. It'll be a reach from teh NYC area and who know what hassles you'll run into as a Swede crossing from Canada into the US with a US registered vehicle.