All Handguns should be banned, there's no practical use for them, most gun crime is linked to them (not tacticool AR-15s) and they're too easy to conceal.
There's a myth going around that guns are all banned in places like Europe and Australia and it's impossible to get them. Not true, there's just reasonable checks.
Here's what I think should happen:
Disclaimer: I get how the US political system works (or doesn't work), just throwing an idea out there that isn't on either side of the argument really.
If you want a gun, you can apply to get a shotgun or a rifle, where you will have to be show to be competent enough to own one, as well as have the correct reasons (hunting, security, sport, etc) and credentials for said reasons.
After background checks, mental evaluations, and extensive training regarding storage and usage (don't point at anything that you don't want dead, etc), you will then be issued a license to buy and own that weapon.
The weapon will then be kept in its own safe, and regular inspections should occur to show that the firearm is kept in the right condition. If you want to sell on your gun, it has to be to someone who has a valid license.
There should also be a marker to track all firearms obtained, in the same way to a license plate on a car. Heck, you should even get touristy ones if you'd like!
As a short aside, I actually think the quickest way to enact any gun control changes would be if a large amount of Black, Hispanic, and Muslim people started to open carry in traditionally white areas. Of course, this won't happen as all these people would get shot, but still. The last time a bunch of minorities open carried in a government area, Saint Reagan himself signed a gun control act!