Hello,
A router, by definition, is a device that connects two networks together. Either from a private 10.x network to a public network, or from a private 10.x to a private 192.x, or any combination thereof. If the IP address on one side is on a different subnet than the IP address on the other side, you have a router.
What your question is really asking What kind of router do I need for a 100 node network? Well, the answer/solution all depends on what kind of performance you would like to have on the network. If you have a bunch of devices using UPLINK ports, and then come to the network router, your clients are going to suffer.
The following is an example. Note it may not be the best solution for what you are looking for:
* Have a router / firewall (one device can do both) to start out with
* Determine if there are any public-access machines that need inbound access, such as a mail server, or web server. This area is known as a DMZ, and while it is not as locked-down as the internal network, it does receive protection.
* Have a 24-port switch for each classroom/lab. Uplink that data to a "master switch" that also has your servers on it.
* Have the master switch talk to the router.
Ideally, you will not have more than 3 - 4 hops between your internet connection and your end device (computer). Otherwise, you risk being able to order a pizza before that web page completely downloads. Also remember that 10/100 base T Cat 5 cabling is only good for 100 meters, and that assumes that your wiring crew maintains the crucial twists in the wire. No twists, and your cat 5 rating goes out the atmosphere.
Oh, and if you don't want to get specialized hardware for a router, you can use a simple linux box with 2 NIC cards installed. You can have the linux box do the routing, along with firewalling and DMZ management.
I hope this helps.
Christian