Have been photographing School’s for many years now and I have found that your camera body should be priority 2 whilst your lens selections should be paramount. As school’s have so many different environments to capture, whether it may be classrooms, outdoors to dimly lit auditoriums and halls, selecting lenses which are able to capture challenging low light situations would be best.
I would suggest a mirrorless option to keep the weight and body size to a minimum such as a Sony A7III or A7IV paired with 2 lenses, 24-70 F2.8 as a general run around lens (can be Sony or third party brand to keep the costs lower such as Tamron) and a 70-200mm F2.8 as a telephoto for everything else. The telephoto lens is a great option if you need to be at the back of the audience to not get in the way of people’s viewing or for sports etc.
An investment now in the correct equipment would set you well for the next 3-5 years easily.