There are national instant background checks for both rifles and handguns through out the US (federal law). You also have to fill out 4473 form (also federal law). Felons don't get any firearm, period.
All of it is useless of course and does not stop or even slow down criminals in the slightest which makes me wonder why we don't just go back to following the US constitution?
A well regulated militia being necessary to the security of a free State, the right of the People to keep and bear arms shall not be infringed.
And do away with all of these federal laws.