By and large, VA has such a favorable climate, the breed really isn't going to matter much, particularly if eggs are your main concern. I live in Prince Edward County in the center of the state, with typical VA climate of muggy, humid summers and fairly cold, wet winters. I've been very pleased with four of the five breeds I've owned. Having a tiny lot that I wish to be a micro-farm, I focused on the following dual purpose breeds: Dominiques, which you could call the "original American domestic chicken" since it's what evolved from the Jamestowne colony. Small for a standard breed, but very hardy, a little flighty, and lays well and consistently. Rhode Island Reds have been fantastic for egg production, and grow to a decent size, bigger eggs than the Dominiques, mine are fairly calm disposition. Plymouth Barred Rocks, another dual purpose bird, decent egg production, but seem better suited to meat production IMO; the roosters were the most aggressive I've ever had. My Welsummers are slow layers, but lay more consistently during the winter than my other birds. The Ameracuanas, or Easter Eggers, have been all around disappointing; though very hardy to the elements and very pretty to look at, they had pathetic egg production in both amount, consistency and size. I thought they would have good qualities from the mixed genetics, but I was wrong.
Anyhow, as far as the climate goes, with a good coop and well fenced chicken run, you can't go wrong with breeds here. Not too hot and not too cold in VA. Get whatever you want, but for eggs and lots of them, just stick with production variety Leghorns or RIRs. They may not be as fancy looking, but they'll keep you fed!