It depends on what the charges are. If they are traffic laws or minor convictions (Not including alcohol, drugs or violence), it might not matter. Like another poster said, call the state police and they will be able to help you out better.
I can't help much with VA but as others have said call whoever is in charge of issuing permits and ask them. Be truthful about it.
My CWP instructor in SC was telling about a student that had a DUI and called. The lady told him that there was a time limit and he needed to wait two months. If he had applied right then he would have been tunred down and lost his application fee. By waiing two months he was approved. I seriously doubt they are going to put you on any watch list for calling and asking.
You may have an issue getting UT if you elect to get one as UT becomes may issue if you have any convictions unless they are well aged. You will also have an issue getting ME as any misdemeanor is a prohibiting condition.