Concerns after using migration assistant

Hi there,

So I'm feeling pretty stupid right now. I'd been teaching at the same place for many years and used a macbook provided by my school. The school was fine with it being taken home over the summer and I probably got a little too comfortable with using it (I didn't use it for anything bad and this isn't the point of my question anyway). When I resigned from the position at the school at the end of the year, I splurged on a brand new MacBook Air for myself because I'd gotten so used to using a Mac and would need to return my school-issued Air.

I should have done a clean set-up, but I didn't know the best way to get all of my important files and apps on my new laptop, so I set it up with Migration Assistant.

I have a few concerns, and I'm sure there are other things I should be worried about that I haven't even thought of:

1. Although I don't really think it's likely that there was any, could Migration Assistant have moved any kind of remote monitoring/tracking that the school had installed? To put it another way, if the school was tracking/logging activity on the school-issued Air, would it still be tracking/logging activity on my new Air?
2. When I look at the Advanced Options for the Admin account on my new computer, it says that it belongs to the User group "staff". Is this anything to worry about?

Would it be best to just save my files to iCloud, wipe the Macbook, and start over?