Those dates are probably about right for foliage, though the timing does vary from year to year based on the weather, etc. Traditionally Columbus Day weekend is the "peak" of foliage season, at least in terms of tourists if not in terms of colors.
I would recommend reservations, definitely during the weekends but it would not hurt during the weeks as well.
It seems you've picked cities to stay in to see foliage. While there's nothing inherently wrong with those cities, there are more trees, generally speaking, where there are fewer people. If you mean rather staying in those general areas, that might make more sense.
In Burlington proper, the only campground I know of is North Beach campground, run by the city. The campground itself is decent (in the sense of acceptable) but in no way exceptional. The beach is very nice and popular, and the park is right on the bike trail that extends roughly along the shore of Lake Champlain for many miles. There are a couple other (private) campgrounds in the greater Burlington area.
If you don't need hookups, there are a number of pretty Vermont state parks. Mt Philo is in the general Burlington area and has nice views from the top, and at least a couple of the sites would be usable with a 19' trailer. The auto road (that goes up the mountain and also serves as the access to the campground) is tight and twisty, but should be doable with your RV. Do be aware that, unlike most of the other Vermont state park campgrounds, there is no dump station at Mt. Philo.
Another good option not near Burlington are the handful of state parks around the Groton State Forest, which has a network of hiking trails that are not too difficult and would be lovely in the autumn.
North Conway in particular can be somewhat close to a giant parking lot during the peak tourism times, with a lot of heavy traffic and many outlet malls, etc. to entice people. I would recommend not staying in that area, but rather finding a campground in some other town in the White Mountains. The white mountains are a beautiful area, foliage or not.
I don't know as much about the Augusta area. You might also want to consider the Adirondacks of upstate New York; there are some very beautiful areas there, too.
Do be aware that the weather can be rather variable in New England at that time of year. (That's true year round to some extent, but the variation is larger in Spring and Fall.)