Clean Install/Privacy Violation?

Long story short–a mix up with my high school occurred. They thought my personal laptop was a school laptop and set it up as a school laptop–with an administrator and student account, preferences for the school's wireless etc. I am not 100% sure everything that happened to it.

The tech support restored my computer and account and everything seems fine (but I did have trouble getting onto my home wireless). Point being is that I am paranoid some of the schools tracking software or software in general might be hidden away on my laptop.

Am I being paranoid? I feel violated and when I use my laptop I feel uneasy. I feel like whether or not there is something on it, I will have to wipe it to feel at ease using it again.

I have a time machine backup from a couple of weeks ago that will be sufficient and I can e-mail myself the files that aren't on the back up. What is the quickest way to do a complete wipe of the computer and then install my backup. Thanks in advance!