The answer to the "gun problem" is in the 2nd Amendment's "well-regulated militia" clause. We DO have a well-regulated militia today - its called "the National Guard."
We should make joining the National Guard a requirement for anyone who wants to legally own a gun. That way their handling of the gun would be subject to military rules and discipline. They would have to train in the use and handling of a weapon. If they wanted to store a weapon at home, they would have to prove that they were storing it safely. They would have to regularly submit to a military physical AND psychologic examinations.
There would also be a secondary "stimulative effect," as each new National Guard member would earn about $5,000 a year that would get pumped back into the economy.