I think some combination of these proposals would have some positive effect:
1) ban the purchase of ammunition magazines that hold more than 10 bullets
2) allow the police and other citizens to seek a court order to temporarily confiscate guns from people who are deemed an immediate threat to themselves or others
3) expand the federal background check law to also apply to gun shows and online sales
4) require that all firearms be kept locked, unloaded, and stored separately from ammunition, as well as make owners who fail to follow the requirement criminally and civilly liable for actions taken (as a result of said failure) by minors and others not allowed by law to posess firearms
5) ban the sale of any firearm to a person under the age of 21
5) ban the sale of "assault weapon" as defined under HR 1808:
The term ‘semiautomatic assault weapon’ means any of the following, regardless of country of manufacture or caliber of ammunition accepted:
“(A) A semiautomatic rifle that—
“(i) has a magazine that is not a fixed magazine; and
“(ii) does have any 1 of the following:
“(I) A pistol grip.
“(II) A forward grip.
“(III) A folding, telescoping, or detachable stock, or is otherwise foldable or adjustable in a manner that operates to reduce the length, size, or any other dimension, or otherwise enhances the concealability, of the weapon.
“(IV) A grenade launcher.
“(V) A barrel shroud.
“(VI) A threaded barrel.
“(B) A semiautomatic rifle that has a fixed magazine with the capacity to accept more than 10 rounds, except for an attached tubular device designed to accept, and capable of operating only with, .22 caliber rimfire ammunition.
“(C) Any part, combination of parts, component, device, attachment, or accessory that is designed or functions to accelerate the rate of fire of a semiautomatic firearm but not convert the semiautomatic firearm into a machinegun.
“(D) A semiautomatic pistol that—
“(i) has a magazine that is not a fixed magazine; and
“(ii) does have any 1 of the following:
“(I) A threaded barrel.
“(II) A second pistol grip.
“(III) A barrel shroud.
“(IV) The capacity to accept a detachable magazine at some location outside of the pistol grip.
“(V) A semiautomatic version of an automatic firearm.
“(VI) A manufactured weight of 50 ounces or more when unloaded.
“(VII) A stabilizing brace or similar component.
“(E) A semiautomatic pistol with a fixed magazine that has the capacity to accept more than 10 rounds.
“(F) A semiautomatic shotgun that—
“(i) has the capacity to utilize a magazine that is not a fixed magazine; and
“(ii) does have any 1 of the following:
“(I) A folding, telescoping, or detachable stock.
“(II) A pistol grip or bird's head grip.
“(III) A fixed magazine with the capacity to accept more than 5 rounds.
“(IV) The ability to accept a detachable magazine.
“(V) A forward grip.
“(VI) A grenade launcher.
“(G) Any shotgun with a revolving cylinder.