Go slow - don't expect to average more than 30 mph. The scenery is fabulous, so you don't want to rush anyway. Some of the scenic pull-outs will be tight for a big coach, though, unless they happen to be empty when you get there. That's not likely in the nice weather months.
Campgrounds on the BRP itself generally do not have hook-ups or much in the way of amenities.
There are some low tunnels at the extreme southern end - you may have to stick to the center of the roadway to transit those. There are two tunnels that are just over 13 ft even at dead center - these may be tighter than your nerves can handle. There is a list of BRP tunnel locations and min/max heights here:
Blue Ridge Parkway tunnels - Wikipedia, the free encyclopedia
It can be very foggy on the BRP at times and it is really white knuckle time if it is. I suggest getting down off the BRP as quickly as possible if you begin to see fog. We got trapped on it one foggy afternoon, but finally found a campground we could hole up in for the rest of the afternoon and evening.