I would be totally fine with these laws. How do gun owners feel about these laws? Are they totally unacceptable or are gun owners as a group, willing to concede something so that less blood is on the ground? Of course no one wants more restrictions. But are gun owners willing to consider something comprehensive? If it is not at a nationwide level, the laws are pretty damn useless because the loopholes to get guns, a truck can be driven through them.
1) Nationwide law that people go and pass a background check (criminal, mental) before being able to buy a gun. As part of that the FBI and state law enforcement need to create a useful database so this can be done. You don't want people who have say domestic violence orders active, as well as people with warrants, etc.
2) That there is a record of gun owners and their guns. You can't really have 1) but then not have a way to show that a background check was done.
3) outlaw semi-automatic rifles. I would even be OK keeping them legal, as long as were only used as a recreational weapon at a shooting range, and that they are stored there. That way it would be like someone wanting to drive a race car. You can have fun, go to the racetrack to drive it, but leave it there. No reason to bring it home with you.