From someone who is a gunowner, and someone who doesn't want to loose that right, I think that regulations that make guns so they cannot be modified, or harder to be modified is a great idea. Fully automatic guns are illegal, and to me, it makes sense to make it as difficult as possible to convert a gun to be fully automatic.
One of the things that I struggle with is defining, in technical terms, what makes a gun more dangerous than another. We try to put it in terms of size of magazines, and semi-automatic, but there are some blurry lines there. If you were to limit long guns (rifles, shotguns) that have removable magazines to only having say 6 shots, that has no impact on hunting. But, I don't know if that makes sense for handguns, when the people that own them have them for the theoretical use of home defense.
I do think that anyone that buys/owns a gun should be required to have taken a safety course. Hell, I had to take a safety course before my dad let me go target shooting with him when I was a teen. That is common sense to me, and something that should be easy to do (in today's political climate, nothing is actually going to be easy). Background checks are good, but that system already exists, and people still get by it. So somehow there needs to be better integration with mental health, along with a very defined definition of what it means to have mental health issues that preclude gun ownership. Gun registrations is something that I wouldn't be comfortable with, but at this point, if you're going through a background check, that does exist. I also think that there should be laws that hold gun owners responsible if their weapons are used in a crime or an accident, and it is determined that they did not properly store and lock their guns.