We were unable to find any restriction for a teen buying and insuring a car in his or her own name in Virginia. However to make certain that the VA Department of Motor Vehicles allows a 16 year old to title and register a vehicle in their own name we would recommend that you contact the DMV directly and request information on this topic.
As for insurance, since you are a minor insurance companies normally will require that a parent or guardian will need to sign on your insurance policy with you since it is a legal document.
For quotes on Virginia auto insurance follow this link.