Women’s head coverings

I have recently begun teaching at a private orthodox school though not religious myself. I have Orthodox Jewish family but didn’t really grow up with it and don’t practice. However, I’ve been getting a lot of questions from the kids because when asked, I simply say, yes, I am Jewish; but I am the only married woman on staff not covering my hair (there are non Jewish teachers and they are fine with no head covering as long as tzniut modest dress).

I have decided I would like to at least partially cover my hair and would greatly appreciate suggestions on scarves that might work, and whether it would be acceptable to partially cover? Thank you!