Unless you know what you are looking at, I suggest buying new. You can get a good quality rifle and scope that will last a lifetime for $800 to $1,200. Most new factory rifles shoot well, and you will generally not go wrong with Ruger, Winchester, Savage, Tikka, Howa, Remington, or any of the other major brands. I think a quality scope makes a bigger difference than the rifle. You can get a great quality Leupold or Vortex new for under $500. I suggest a variable in the 2-7, 2.5-8, or 3-9 range with a 40 mm objective. Hunt with it on the lowest power, and only turn it up if you have time. People tend to buy more magnification than they need at the cost of spending more money, more weight, and too small a field of view for close shots such as are likely in the Virginia woods. If you are interested in aesthetics, wood and blued steel rifles are generally more pleasing to the touch and to the eye, and don't require appreciably more care than synthetic-stocked stainless rifles. Stainless rifles will rust if not taken care of, they just don't rust as soon.
Unless you plan to reload, choose a caliber that is common and for which you can find a wide variety of ammo. If ammo is affordable and easy to come by, you will practice more. If you are not planning on hunting anything larger than deer or black bear, a 6.5 Creedmor is a great option, and will do for elk if you pick a good bullet and a reasonable shot. If larger game such as elk are likely to regularly be in the mix, other good options to consider are the 7-08, .308 Winchester or .30-06. A common mistake is for people to look for the lightest rifle. Unless you are backpacking in, a rifle in the 7-1/2 to 8-1/2 pound range with scope is a good compromise between shootability and carryability. A heavier rifle that is well balanced will feel lighter than a lighter rifle that is poorly balanced. Light rifles are harder for most people to shoot well and are generally less forgiving of shooter inconsistencies in hold and position, as well as generally being pickier about what ammunition is accurate in them. Do not be tempted to get an magnum as a first rifle, as they are more more expensive to shoot and harder to shoot well due to noise and recoil. Go to your local big-box sporting goods store or to a large full-service gunshop and handle a bunch of different rifles to see what feels comfortable in your hands and seems to shoulder naturally for you, not all rifles fit all people. If you are left-handed that will reduce the options, but there will still be plenty. After you find something that feels good, spend some time researching that make and model before actually putting down your hard earned money.
Hope these suggestions help.