I'm going to differ with the other posters about your route. We drive it frequently as we have a daughter in Valdosta, GA.
As a new M/H driver I'd suggest the following route to avoid as much traffic as possible.
I-95 north to I-26 toward Colombia, SC. Then I-77 north to I-81. I-81 thru the Shenandoah Valley to I-78 into NY. From there you're on your own as I don't do NYC in car or RV.
This way you'll miss the Richmond, VA to Philly mess and get a chance to get familiar with your rig.
I do the Beltway around DC going to Annapolis and it is awful in a M/H.
A good stop outside Savannah, GA is Skidaway SP. Big sites and very pretty and quiet.
RocK Hill, SC is just south of Charlotte and has Ebenezer County Park which is nice.
Mt. Airy, NC has Mayberry Campground. I've not stayed there but it gets good reviews.
Take your laptop with you and then use www.epgsoft.com
to pull up campgrounds.
When you get confused in campgrounds, ask a neighbor questions. RVers are friendly and glad to help.
Be prepared to have your jaw drop at Lazy Days. Absolutely enormous. They'll feed you and your wife breakfast and lunch every day in their dining room, FREE! They have 273 service bays for an idea of how big it is.
Most important; HAVE FUN!!!
Take your Golden Access pass as many government parks accept that IF you ask.
I'd say no more than 300 miles. Stop well before dark so you can get all set up and settled before dark. In unknown areas I usually start looking about 2-2:30 for a place to spend the night.
If I'm going to have stuff in the fridge I leave the propane on except when fueling or for tunnels that require it to be off. You can leave the doors closed and it will stay cold for several hours.