This is a divisive topic.
The reasons for gun restriction and the reasons for allowing ownership are all valid.
I think the main arguments for low restriction gun ownership are protecting the people you care about, dissuading government control, and because of the constitution.
Some people have said that the constitution shouldn't apply because it is outdated, or just plain wrong. I don't agree that it is wrong. The constitution gives a completely valid reason for owning a firearm: a well regulated militia. Switzerland is one of the only countries today with a militia, and it has gone well for them. They have one of the highest gun ownership rates in the world, and one of the lowest gun-related crime rates worldwide. The government issues weapons, and trains people in their use. This works because everyone has weapons.
However, I don't think this would work in the United States. For one, we're not a very cohesive population. There are too many difference that cause hatred. Switzerland is a small enough country that they can be considered a nation-state (when the nation(culture, language, religion) coincides with the boundaries of the country), and there is less tension.
I don't know how well a non lethal self-defense weapon would be. I think fear of death is the big thing that could prevent other violent crimes. We already have things like tazers and these:http://gizmodo.com/this-clip-on-handgun-attachment-makes-bullets-non-letha-1730039256 but not much has changed.
I don't know what a solution could be, but these are my thoughts.