People should still be able to own guns, but they should need a valid reason (such as hunting or farming). Shooting people (this includes self defence) should not qualify as a valid reason.
This is how it works in most developed nations with sometimes quite high rates of gun ownership (0.2+ per capita) but without the endemic gun violence of the US. It's worth noting that these sorts of restrictions effectively rule out ownership of handguns - and concealed handguns (real or imagined) seem to play a major role in most police shootings of innocent people in the US.
I think Police training needs to be changed significantly as well though. Training Police to de-escalate situations, and to deal with normal people who are scared, in danger, and unpredictable but not malicious - this is the significant majority.
Police in America seem to act like soldiers, and forget that the people in front of them deserve protection as much as everyone else, not least because they are innocent until proven guilty in a court.