From the White Mountains/Franconia notch area of NH to Lake Champlain, the obvious route (and it's a good one) is to take US 2 until you reach I-89, at which point you could reasonably take either road; they're mostly in parallel. US 2 is a common truck route, so no impossible bridges or corners.
Apple Island Resort is a pretty nice place in the Lake Champlain islands. The City of Burlington has a campground at North Beach that's possibly also worth consideration; the beach is lovely for swimming, and the campground is right on the Lake Champlain bike path, but the sites are somewhat smaller and closer together and I gather sometimes things can have a bit of, well, youthful exuberance.
Most of the Vermont state parks have limited sites that can accommodate large rigs, and none have hookups (most have dump stations and fill stations and bath houses). If you're interested in staying at one, I would suggest calling ahead and making a reservation over the phone. The rangers/employees will have a better idea of what sites you could fit into than the web reservation system.
You might want to think about heading back through the Adirondacks of New York; there are some absolutely beautiful areas there. Mind you, I'm not suggesting that Vermont is lacking in beauty.
For heading south from Lake Champlain through Vermont, I usually take US 7 to VT 22A to US 4 to NY 149 to I 87 S to I 90 W to I 88 S and on to I 81 S. When you take I 90 between I 87 and I 88, there's no toll charge.
