The router is used for connecting to the Internet. The office's switch is connected to the router, so the offices and the classrooms get Internet. The cable that are used for the computers is Cat. That's the highest of the categories, because the wires bandwidth is 100 Mbps. You should definitely use Ethernet.
Ethernet is the most popular architecture used when building a network.
To send information, each computer on an Ethernet network waits for a pause on the network. But, if two computers try to send information at the same time, then a collision occurs, so the computers must try again to send the information. Ethernet is not that expensive. The speed of Ethernet depends on the type of Ethernet network used. Most offices would use 10 Mbps.