The last option is to contain the area and use a negotiator to deal with this issue. With the first three option the chances of someone getting hurt or killed is extremely high.
As the negotiator I would want to try to contain the hostage taker to the smallest location in the building or exterior area and attempt to deny the opportunity to observe the police presence activities.
My first and primary precaution is the safety and well being of the public. This incident is on a Friday at 3:15 pm so I could assume that school has let out or in the process of releasing students from this middle school. In addition to the school there is also a public library that could be busy. So it is my duty to make sure that all parties are safe, so I would request an immediate lock down of both buildings. I would also place uniformed officer on the street near those buildings. I would request that a release to the press happened so parent would not panic and drive to the school to get their children.
In a prolonged stand-off individual begin to become fatigued and need to have a change out. So at some point I would request that the officers that have been there for an extended period of time be relieved of his or her duty and replaced by another officer. One of the issues with doing that is that some important information may not be conveyed to the oncoming officer so there could be a break down in communications. In addition to the officers I would start to