Personally I see arming a good percentage of the administrative and teaching staff of the school.
They are always there when the students are there. No one other than the staff need know who on the staff is armed. Actually no one other than the school board and the administrative staff need to know who is armed. The fewer the better.
The teachers could be paid a bonus to their salary for taking the training and carrying the weapon similar to the extra pay teaching coaches get.
The panic button would be a good additional measure however the extra cost to the school could be prohibitive. Anything like that designed to school specifications is always going to be much more expensive than the simple civilian package.
School Marshalls. Much like Air Marshalls.