Clinton-era Treasury Department Official (remember, ATF was part of Treasury until the Homeland Security Act) Susan Ginsburg lays out some good ideas on how to fit gun violence into a broader strategy of crime control. You can safely ignore the gun pedants (my new favorite type of internet troll) in the comments.
The main issue from a crime control perspective is not the existence of this or that type of weapon, but instead the fact that criminals are able to acquire weapons easily through private transfers, and that the chain of ownership of those weapons can't be traced. Closing the "gun-show loophole" by requiring all sale or transfer of guns to include a background check on the purchaser, would help a lot. Next up would be undoing various efforts to hamstring the Bureau of Alcohol, Tobacco, Firearms, and Explosives (formerly just Alcohol, Tobacco, and Firearms or "ATF") that were enacted during the Bush years. This is not to say that we should go back to the days of undercover agents enticing individual citizens to make technical violations of firearms laws. We should, however empower the agency to be more vigorous in ensuring that firearms sellers maintain good records, enabling law enforcement agencies to track over a longer period of time. The ATF has been understaffed for some time and cowed by a combination of approprations riders and the threat of Congerssional hearings from being more vigorous in -- well, in just about anything. I'm not an expert in this field by any means, but based on my reading of various CRS reports and other documents it appears that the vast majority of dealers are doing their part on the paperwork front, and that the problem is concentrated in a handful of unscrupulous dealers. Last but not least would be to speed the synchronization of various records of criminal and mental health histories. For instance, Colorado currently synchronizes the list of civil commitments for mental illness with the state's firearm registries every six months. Getting all relevant data to the NICS background check system in a more timely fashion will reduce the risk that someone who should fail the check will slip through.
The second question is whether or not it's worth reviving the ban on specific weapons. As Ginsburg points out, the 1994 Assault Weapons Ban didn't go far enough in two directions: the rules on what was legal and what wasn't had nothing to do with risk, and existing weapons were grandfathered in. To solve both problems, Ginsburg tries to make a category of weapons that ought to be regulated based on how much danger they pose. She suggests creating two new class of weapons under the NFA: one for any semi-automatic long guns that will accept high-capacity magazines, and another for semi-automatic pistols that both accept high-capacity magazines and certain calibers of bullets most commonly found in military weapons. Rather than ban and buy back these weapons, they would be subject to stricter regulations, probably something similar to but slightly less stringent than the rules governing fully automatic and selective fire weapons today.
The first set of reforms—the tightening of record-keeping and reporting requirements, putting an end to hamstrings on the ATF—are basically no-brainers that won't even affect a majority of gun owners. The second is more politically difficult, especially if handguns are included. An NFA-style regime for these weapons would be less onerous than an outright ban, and would eliminate the problems caused by grandfathering in existing weapons, but still might be annoying enough that no one wants to enact it.