I do a lot of work with schools too. Loads of good advice above - often the non-posed, almost more 'reportage' shots are better than posed photos, especially for primary, where kids don't understand the concept of not posing, so pull awful huge smiles.
School visitor badge stuff is complete standard fayre. I don't always have an admin person with me, depends on the school. (yes, I am CRB'd - but that's an irrelevant debate)
I shoot a lot of wide apertures.
Lots of key things to look out for - the school probably also has a few key 'attributes' eg 'friends', 'caring' sharing' etc etc usual stuff - try to think what images will work for these. Other things that are always good are stuff like 'teacher helping student' or 'two students working together' - look for where students are interacting and talking to each other.
If any kids CAN'T be photographed, have them put a sticker on their jumper, or for secondary, mention it to them.
In classrooms, I often use a single speedlight slightly warmed up, popped off the ceiling just to up the contrast a bit from what can come in the windows.