"A well regulated militia being necessary to the security of a free state,
the right to keep and bear arms shall not be infringed."
The first phrase, usually overlooked, sounds a little puzzling. But it is easily understood in the context of the times. The fledgling United States had only a small federal government, and could not afford a standing army suitable to its need. So in 1792 the government passed (one of a number of) militia acts: this one required all able-bodied, law-abiding male between 18 and 45 to join their state's militia, to provide their own guns and supplies, to require them to be trained (well regulated), and be subject to mobilization in time of war -- and, according to the Constitution, to be under the ultimate control of the federal government.
Some of this could be reinstituted. My first thought is that those who purchase or obtains guns (legally) be members of the NRA or a similar organization, that the NRA would be responsible for background checks on such individuals (perhaps with federal dollars) AND be held liable if a gun crime is due to inadequate checks. The same NRA or such would also be responsible for hold gun training/safety programs, which would be mandatory for owners. Most important, gun owners (I would make exceptions here) would be available for call up and mobilization in times of war -- which, however, would only be done as a last resort measure as we are not (for the most part) dealing with professionally trained and equipped soldiers. I would also drop the mandatory gun ownership from the 1792 act.
With rights come responsibilities, as we all know. This is just an initial proposal and I invite debate and discussion on it.