When a Citizen registers for Selective Service, require firearm instruction and mental screenings prior to gun purchase.

At the age of 18 an American is required to register for the draft. At that point we should evaluate each Citizen for their fitness for that role. That would include basic firearm safety and mental health screenings. Each passing Citizen is then given an ID Card necessary for the purchase of a firearm.
Since attendance is compulsory, including Citizens who will not purchase a firearm, the possession of a Card does not signify the intent of purchase. This process creates a more stringent control that will help ensure that only responsible citizens purchase firearms.
This plan calls for compromise while calling for more stringent controls it also demands all Citizens go through the process. That way Gun Control Advocates get stricter laws while Gun Owners get to keep their anonymity.