I don't have great recommendations, because relative to this specific incident, I have no solutions and given US law and history, I don't think there is one. The firearms were legally purchased and registered - by the mother, who the shooter killed, and then essentially stole the firearms.
According to today's reports he actually broke into the school to carry out his evil thoughts...so security short of police on full time guard at every school door plus locked, barred gates and classrooms in schools (an impossibility based on political, budget and logistical reasons) there was no way to prevent his entering.
Where is the remedy? Confiscation of firearms is not only politically impossible (and something I would not support), it's also logistically impossible. There are millions of firearms in this country, probably more of them old enough to be unregistered than those which are registered. In fact, about 10 of them are in my basement...I think there might be federal paperwork on 2 firearms I own.
It is logistically impossible to disarm the US citizenry because of the number held in private hands, and they would not agree to an attempt. You will never - and I repeat, never - disarm the US population. Can't be done. And as long as there are firearms held by the public, there will be a source of firearms for those who wish to steal them or acquire them illegally.
It is also true (IMO) that many crimes and injuries are committed by people using firearms either stolen or acquired privately with no registration. One could require registration of private sales (although I think that even that might be political suicide for elected representatives making the attempt), but those with evil intent can ignore the law and keep stealing or buying them off the records. As I noted, there is an immense pool of available weapons that only require theft or illegal purchase.
And note: the fact that the firearms in Connecticut were registered made no difference, nor did it make a difference in the Columbine school killings. Registration is NOT the answer, because the act of registering a firearms only makes it traceable after the event takes place. And it is not clear yet, but it sounds like all the shooting was done with two good quality semi-auto handguns, and that the Bushmaster .223 rifle the shooter had was unused because it was left in his car. Banning "assault rifles" (a vague term with no possible accurate definition) isn't the answer either, at least in this case. Banning large magazines isn't either, because as this example showed, they aren't even used in many cases.
Perhaps the way to MITIGATE (not prevent) such events is an effort to prevent anyone who has any record of criminal behavior, mental illness, or perhaps even some types of mental challenges (the shooter evidently had autism) from legally purchasing a firearm. It won't entirely prevent crimes or shootings, but it might reduce the number of mentally ill and antisocial people who own firearms - slightly. That might in turn somewhat reduce the number of shootings by people with mental illness - but not by those motivated by more common criminal motives such as drugs or gang activity.
I am attempting not to make a political argument, but a logistical one.