Here's how I would run it.
1) Solicit teachers that would want to do it for a bump in pay.
2) Have the State police run the back ground checks, and handle the threat assessment and firearms training. People like to think that the teachers wouldn't be able the guns as efficiently as police, but that's non-sense. Firearms training is only a small piece of police training, and could be taught to a police standard within a few hours.
They'd also have to requalify every few months, much like police.
3) Ideally, but not required, the pistols would be in the hands of administrators like Principles, vice Principles, Deans, etc.... to limit direct contact with the kids.
4) Pistols are to be carried IWB and frangible bullets like Glaser safety rounds or Magsafes. This would be done to limit discussion and apprehension from the kids about the pistol. The bullet choice is simply out of safety concerns should the firearm need to be used.