This is all just conversation starter.
1. At the minimum make purchasing assault style weapons a long, thorough process. You want an AR-15? Be dedicated to it over months including training and tests, at minimum as difficult of a process as obtaining a driver's license.
2. Any gun purchase, person to person, store, show, etc. must include a background check.
3. If you are convicted of any violent or destructive crime, no guns. Domestic violence, no guns. Battery, no guns. On and on. Maybe even some temporary suspensions of gun ownership similar to getting a DUI for certain offenses. Get a DUI, no driving for 6months to a year. Something similar where you have to turn in your guns for 6 months to a year.
Responsible gun owners only suffer in the short term (longer waiting periods, having to take a course and pass a test) but not in the long run. Added to that, as a whole they would be more educated. Gun owners as a group would also be more respected and trusted in this country by those who do not own guns by starting to eliminate people who become problems from having legal access. Guns are a right but like others rights in this country they can be taken away if you f*%# up.
I've addressed guns, now "mental health"
Any mental health related issue is covered by a single payer government mental health care plan. It's there if anyone needs it. The people who can't afford it are usually the most susceptible to it turning into a negative consequence for themselves and others. Not having access also can lead to not being able to afford it down the road when the problem turns to a crisis.
Nothing will ever completely prevent violence and gun violence, but we can greatly reduce the likelihood.