I might sound like a raving soicalist with this one, but I could actually see mandatory firearm education and the registration of a gun owner...
Let me explain.
I believe in a "well regulated" public in the sense that gun owners should have a basic understanding of firearm safety. In the past, that wasn't much of an issue because more people were raised with firearms, or were drafted and received military training, etc. I have never been on a military range where I felt particularly unsafe (with the exception from a "short" 203 round one time). However, I have been on several civilian ranges where it was obvious that a firearm owner or two had relied solely on Hollywood for their education. Barrels casually waving around with fingers on triggers, little attention to hands off during cease fire, rounds down range during cease fire, holes in places that indicated too many accidental discharges, etc. In some cases there was a range officer to take care of things, in others not. Most shooters, if not all, have had similar experiences.
So, I don't have a major problem with licensing the gun owner after passing required, reasonable and appropriate safety courses, and revoking that license for irresponsible behavior. A responsibility goes with the right type of thing. Registering the owner is different IMO from registering firearms because:
1. Let's say America is under a police state rule. As a registered gun owner you turn in that rusty old .22 to the collection point like any good citizen would. They do a surprise inspection a few weeks later and find nothing in your house "I understand the need officer, thanks for being so careful with my belongings during the search."

Meanwhile, my FNFAL and 3000 rounds of good South African 7.62 are buried in a sealed container on some remote property.
2. It's not like that anti-gun neighbor of yours, who fully supports the current regime, wouldn't drop the dime to the Alphabet Ninjas and mention that he once saw you carry a gun case into your house a few years back. Registration or not, people know your business all too well. Remember, the Gestapo did very little original case work (totally lacked the manpower for that), they just sifted through the leads provided by the good citizens of Germany for those that were the most interesting.
HOWEVER... I would only approve of this were our 2nd Amendment rights far more clarified in the modern era than they are now. As it stands, anything that would give the anti's more leverage without guarantees in return is not worth the effort, and will only be misused and abused.[edit: Of course, most Americans would already have received this firearm education while in High School, as a standard elective like driver's ed and with federally funded Civilian Marksmanship Program after school shooting competition

]
Felons -- if violence was involved, especially with firearms, I see no real need to give them a right they threw away when the committed the crime. Especially, if there are "anger management" issues at work, REAL domestic violence, etc. Of course, in a sane world the prisons would not be crowded with nonviolent offenders, there would be no useless and misguided war on drugs, and true sociopaths would be locked up for the full term of real sentences. It probably would be much less of an issue.
Automatic Weapons -- I would like to see them more available. However, I wouldn't necessarily do away with having a rigid background check requirement and perhaps the current tax structure enhanced to make up somewhat for lower prices due to greater availability. I realistically do believe that a fully automatic assault weapon is more deadly than a semi automatic rifle, and should be harder for a potential nut job to purchase for his grand, public exit. Still, they should be easier to acquire than they are today for the average, law abiding shooter and collector.
The Founding Fathers did prohibit ordinance, and I feel that these start to move into that catagory, clearly beyond any semi automatic weapon regardless of magazine capacity. Nor is automatic fire a requirement, initially, for armed resistance. Still, wothy of a reasonded discussion since I certainly would like to be able to afford, own and shoot an MG42 or a PPSH 41

Charon