Automatic weapons are hard (and quite expensive) to obtain legally. Semiautomatic weapons are used somewhat extensively for hunting. I believe that includes AR-15 type rifles for smaller game. There are quite a few larger caliber semiautomatic rifles available for hunting animals of the order of deer and elk. Where they have detachable magazines the usual capacity seems to be three to five, sometimes going to ten. The overwhelming majority of handguns, of course, are semiautomatic.
Training requirements for gun ownership makes sense generally, but does not address the problem of someone intent on a rampage killing. There is no reason to think such people are incapable of training, or any clear benefit to improving their skills.
Unless military service is compulsory and universal it probably can't be used as a gun ownership prerequisite. There are quite a few ways one can get a dishonorable military discharge. Not all of them constitute reasons to restrict civil rights after discharge. If I remember the Navy BuPers manual correctly, there was a time when committing a homosexual act could lead to dishonorable discharge.
Background checks have been federal law for some time, without apparent effect on rampage shootings, and the often mentioned "gun show loophole" seems not to be a significant problem, as nearly all guns used in these shootings have been acquired legally, after background checks, from licensed firearm dealers. The problem here seems to be lapses and sloppiness with implementation of existing law.
"Mental health issues" covers a lot of people, nearly all of whom are dangerous only to themselves, if they are dangerous to anyone at all. Something like a majority are not under treatment and therefore likely to be missed anyhow, along with those like the Colorado theater shooter who went fairly quietly crazy shortly before beginning to accumulate his arsenal. Again, restricting civil rights is a serious business, demanding particularized and individual legal process, not simply a relative's (or psychiatrist's) impression that something might be brewing.
There is a case to be made that someone mature enough to vote is mature enough to be a full citizen - including gun ownership and alcohol purchase. There is no proof that the age of 18 or 21 (or 13) is magical, or that the appropriate age is the same for men as for women. I have seen lay articles suggesting that the appropriate age for men might be as high as 26.
Waiting periods might be a good idea, but probably would be most effective in preventing suicide. Spree shooters generally seem to take quite a while and do a fair amount of preparation; they would not be impacted by any plausible waiting period requirement.
Putting armed teachers in schools is not something to be done on a whim. Both civilian and military police officers receive extensive training and are required to requalify periodically. Armed teachers would need to meet the same standards and more: in their environment, they would be called to use their weapon only under chaotic conditions in which it is far too likely that a shot will hit an innocent person or two. The spree shooter does not care, but it would be devastating for a teacher to take out a student or another teacher instead of an attacker. School systems would be far better off to pay close and detailed attention to building physical security.
I doubt that even the most hard core NRA members think spree shooting is a good idea. As a non-member, my impression is that they do not think anything short of universal and fully effective confiscation of all private guns will prevent them, and that they think those who want to restrict gun ownership beyond current limits know it too and are working an agenda that, if completed, will lead to it. They consider that end completely unacceptable, and any step toward it nearly as unacceptable.