I agree with Leo that to give good recommendations we would need to know more about the requirements for each school. In general I would think that each of the labs would need an Ethernet switch and it sounds like a 24 port switch would be adequate. I assume that you would use copper Ethernet to connect the switch to the computer and would want the switch to have at least one fiber connection to connect the switches together. I would think that each school would need a layer 3 switch or small router to connect the lab switches and to provide routing logic. I would assume that the connections between schools would probably be fiber.
You have not indicated whether this network is to operate as a stand alone network or whether it needs connectivity to the Internet. If it needs outside connectivity then there is probably a need for a router for this and perhaps a firewall.
HTH
Rick
HTH
Rick
