Of course, there is a limit to what you can take with you on a teaching assignment; nevertheless, some items are basic.
It might go without saying, but you should carry a pen. School personnel should not have to supply you with one when you sign your pay voucher. The pen speaks to your preparedness for the entire job.
If you catch colds easily, a hand sanitizer might be another basic item for you to carry. Along the same lines, you should have a handkerchief: not every classroom has an ample supply of tissues sitting on the teacher's desk.