I want to set up a fictional network configuration for a school in my neighborhood. They have about 50 computers altogether, 2X20 in computer rooms for students and another 10 scattered around for various professors. They should all access the internet through a dedicated Linux router machine.

What they would like is to have domain names for those three computer groups.

Lab1, Lab2 and Professors.

The computers in Lab2 and Lab1 should have static ip and should all be named by numbers. So there should be 1@Lab1, 2@Lab1.... etc.

And the Professors network should have a DHCP, with authentication.

Is it an ok solution to have all these functions on a single server? (The one which will be used as a router)
Do I have to set a local DNS for domain naming? Do the host names for Lab computers have to be set on the clients, or can they be automatically assigned?