Virginia is a "Shall Issue" state, so if you qualify for a CHP you will get it. Qualifications are on the state police web site.
Private gun sales are legal. I really like that. It makes gun shows more fun and easier to buy and sell at good prices.
I live near Quantico and have a host of great gun shops available to me.
Exactly where you are heading makes a difference... there is Northern Va. and then there's the rest. Traffic in NOVA is unbelievably terrible.