IMO, the PEW Research data provides the best summary of measures and their acceptance by the American public...the easiest ones for inclusion in bi-partisan legislation should be the following..(let's understand that there are always a few fine points to each, but they shouldn't stop all action on them)...
>Increased minimum age for gun purchases (e.g. 18 --> 21, or higher)
>Longer waiting times for all transactions to allow for checks to be made
>Robust databases for registration and checks on qualification in every transaction
>"Red Flag" processes and procedures that act quickly...involving police, school counselors and mental health professionals...could be treated in a "HIPPA" manner so as to not stigmatize people unnecessarily, but for certain, when trained persons become aware of questionable behavior, their needs to be a 'Flag" raised so that no transaction occurs before further review removes the flag.
>Extremely rigid "concealed carry" requirements...the vast majority of gun owners have no experience/training in how to handle a public "active shooter" event...approved CC owners need to be essentially "Pros" in the security arena.
While these measures are essential, they will not keep Psychos with no history of mental illness or questionable behavior from being able to purchase guns, so the best we can do is take the most efficient killing weapons (e.g. "Assault Rifles") away from them, and that means no sales for new ones and buy backs for those already in circulation. This is a sacrifice for responsible gun owners, but hopefully, they realize that they can still go hunting, target shooting and defending their homes with other very effective firearms...a small price to pay for helping to reduce, if not eliminate the horror and terror of mass shootings.
btw, I could build a case for making this country even safer by eliminating all guns in civilian hands, but "Prudential Judgement" says choose dramatic improvement over idealized perfection...and stay there.
Link: https://www.vox.com/policy-and-politics/23141651/gun-control-american-approval-polling