My 16 year old backed into his friend's car. He did 1000.00 worth of denting damage. Would it be best to settle it privately, pay the grand, or does anyone know how much his insurance would go up if we claimed it with our insurance?

Your son is already paying a lot because he is under 25. He will learn much faster to be a careful driver if you don't bail him out, but require him to contribute toward the increasing insurance payments.

I would recommend that your teen pay this off. If he doesn't have the money, if it was my child I would pay the $1K to the owner of the other car, and then I would dictate a repayment plan to my son for him to repay me, perhaps working odd jobs around the house. If you simply bail him out he won't learn how his actions have consequences.