There are three four requirements I would put in place regarding guns:
1. No weapons that can fire more than one round per squeeze of the trigger. It must be illegal to modify a gun to do that, and guns would have to be hard to be modified that way (a shotgun would be hard to do as an automatic weapon).
2. All gun transfers must be registered.
3. A list showing people who cannot own a gun. Getting on the list requires the approval of a judge. A temporary state can be issued by a judge; a permanent entry requires a hearing.
4. (As recommended by #36 KGxvi)An insurance requirement. $500,000 policy for one gun, $1,000,000 policy for 2-5 guns, and $5,000,000 policy for six or more.