What gets lost in the gun control debate is how criminals get their guns. There is some international gun running into the US, but it's relatively small compared to the normal way criminals get their firearms.
Unfortunately, because of strictures put in place by NRA Congressional Champions, it's difficult to actually know how guns flow in the economy. But here I'm going to give a scientific wild-ass guess based on both the fears of gun owners having their addresses published and police reports.
Most guns that end up in the hands of criminals start as legal purchases. These can be straw man purchases were someone with a clean record makes the initial buy from a dealer. They make these purchases with other people's (the criminal's) money, or they sell the weapon right away. The next way is secondary sales, where the criminal (or conduit) makes a private firearm buy (gun shows, classified ads, whatever). The third way is to steal them from legal gun owners.
This is why the claim that regulating what "legal" gun buyers can purchase will have no effect on the weapons criminals get their hands on is complete bullshit. The vast majority of weapons used in crimes or seized in raids started their life in the economy through a legal sale. If you can choke off the supply there, at the first sale, you can affect the weapons criminals have access to.
The NRA and gun proponents don't want you to know about that. Which is why the ATF and FBI can't keep gun purchase records (or they'd notice the straw men and bulk purchasers). It's why no records are allowed to be kept at all. Not so much from the fear of confiscation (although that's what the NRA and it's gun manufacturing drivers use to keep the pressure on).
It's also why you hear in the news that the weapons used by most mass murderers were owned legally by someone (either the murder themselves or a close relative the murder can steal them from). Limit the access for these "legal" purchases and you'll keep weapons out of the hands of criminals.