Q. What sort of control do you believe would have prevented the Charleston shooting?
A. A complex question or loaded question is an informal fallacy. A serious answer is very little if any form of gun control can be said to prevent an act already completed.
"Would have" The question presume the act has not yet happened. Your response is dishonest.
Q. For starters, how about criminal control.
A. Many mass murders and many murders in general are committed by persons with no criminal record.
And so....?
Assume everyone will commit a crime and write laws to treat them as if they have?
However, persons with a propensity for violence (arrests for battery, sexual battery, domestic violence, child or animal abuse) or a history of substance abuse (two or more DUI's; arrests for possession of dangerous drugs or treatment for drug overdose) and persons determined to be a dangerous to themselves or others ought to forfeit their Second Amendment Rights and be denied the ability to own, possess or have in their custody and control a gun.
Welcome to existing federal and state. law.
The only way to enforce this form of Criminal Control is to license every person who want to own, possess, etc. a gun.
Said licensing, while violating the Constitution, will have no such effect.