I am very anti gun, but even I can see that new gun laws will do very little to help the real gun violence. That said, I still think we need to better implement what is already there with universal background checks and get rid of the loop holes for gun show buyers.
Unfortunately what really needs to be done is a better deterrent to crime which is impossible with such a lose definition on the 8th amendment. Violent offenders should be subject to harsher prisons, and I don't mean harsher in the sense of the population they are put with, but rather standard of living type changes. We allows these harden criminals to basically infect any of the other prisoners and make rehabilitation completely impossible. In fact prison almost always has the exact opposite effect. These prisoners should be required to pay back society and that shouldn't be considered a harsh punishment.
With this in mind you could start in acting laws that deter guns being used in any crime. Use a gun in a crime and you don't go to the medium level prison, you go to the shitty Labor Camp prison. Act up in prison and cause issues and you take on more labor. Act better and attempt to better yourself and you get less. No more of this 4000 calories a day and allow them to work out, only making them even more dangerous when they get out. When someone gets 20 years in prison for a crime, currently we think "thats it", when really it should be so bad that people know thats a harsh sentence.