Been discussed many times, but doesn't hurt to re-vamp:
NICS check is good. Except lautenberg must be eliminated to the extent that it traps misdemeanants and those subject to CIVIL restraining orders. And it must be written to put the burden of the check onto the FBI in this way: the law should state that "If the FBI is unable to find a valid reason for denial with 72 hours, and communicate that reason to the FFL within 72 hours, then the FFL shall automatically allow the transfer to occur" or similar.
Draconion gun owner "responsibility laws" - providing for strict criminal AND civil penalties for your NEGLIGENCE, ordinary or gross, which causes your guns to get into the hands of children or criminals, and then harm results (i.e. leaving loaded weapons around the house with children present, etc.). Or when your own negligence in handling the gun results in someone getting hurt.
Draconian enhanced sentencing laws. Add to the sentence when a gun is used in furtherance of the underlying crime (robbery, etc.)
[Not strictly a "gun-related law", but crime-reduction-related, so relevant: Draconian ordinary criminal laws for violent offenders. High investigation rates. High arrest rates. High conviction rates. Long sentences for VIOLENT offenders. Eliminate the war on drugs. Make pot 100% legal like alcohol. Highly de-criminalize the harder stuff, for usage/possession.]
A 1934 Act-style registration scheme for anything weapon larger than a 20mm or using explosives. Still legal with a modest tax, but let's know who has the tanks.
Oh yeah: Mandatory classes in grade school, junior high, and high school covering gun safety / proper gun use, and the second amendment. Optional courses in junior and high school for shooting / competition shooting.
That's about it. Anyone short of children under 18, convicted felons and the adjudicated mentally ill can own anything they want without a license, and carry it anywhere they want without a license, including planes and government buildings. Well, ok, maybe when on the plane or taking the white house tour, you should be required to keep handguns holstered and long guns unloaded.