The Sandy Hook school had a door with an electronic lock , such that ordinary entry required someone on the inside to "buzz you in".
Unfortunately it also featured a large glass pane.
The first suggestion is going to be diffrent for each building and grounds , so improvement in phisical security is not simple , but it is uncontroversial so lets get started on that so that something effective can be begun.
So , bars across all glass panes large enough to enter through, hindsight can be painfull.
Fire safety requires that there be a way to open these bars from the inside , so perhaps a latch that is easy to work but can't be reached from the outside.
Non leathal wepons in trusted hands inside the school , some of the teachers and staff at Sandy Hook behaved with great valor , but they were empty handed. A mace spray or a tazer would have been inadequate , definately , but nothing at all is also inadequate and nothing is all they had on hand.
Lastly Firearms and serious firearms training for some of the staff, I don't think it possible to train and arm everyone , so no firearms without the training program, and no certifacation as a school untill a minimum number of trained and armed teachers and staff are reached.
None of these ideas are origional , just my favoriates.