Your solutions are not as simple as you think.
Your metal detectors are useless without one or more human beings to monitor them and stop those that set off the metal detectors. Those people will need pay and benefits. If you use cops those cops are not doing other cop work.
Your gun sniffing dogs are expensive and require handlers that are also expensive. The dogs also have a rather short life span and an even shorter working life. You never know when a dog will lose its sense of smell or just get bored with the work and just stop doing the job.
Another problem with these ideas is that you have to funnel all of the students through the metal detector and past the dog. This is really going to slow down kids getting in to school. It is also a recipe for concentrating students in to a clogged area where a shooter could just spray bullets in to a crowd and kill lots of kids really quick.
If you had a large school you would have to have lots of metal detectors and since they break down from time to time you had better have a couple extra ones sitting around and a maintenance contract to get them fixed quick.
Nope I think it would be a much better solution to arm half your teachers and have a training program to make them proficient with their weapon.
“I think it would be a much better solution to arm half your teachers and have a training program to make them proficient with their weapon.” But, but, but then we the people are not dependent upon the government! Oh wait ... good idea!