In theory, you should need no other computers than the mock mainframe and whatever you use as terminals. In practice, you'll probably want additional machines for specific tasks. Usually this will be because of security, not performance.
For example, let's assume you have a network with a dial-up connection to the Internet for email and browsing. Of course you could put all the hard- and software required on the mock mainframe and not see much of a performance hit (in fact, if your network is slow, it might even be faster). But that puts your most valuable computer right where everybody who is on the Internet — which increasingly means anybody on the planet — can attack it.
For better security, put a machine between the mock mainframe and the outside world. Make sure this Guardian machine is not only heavily fortified, but also expendable, so if it is taken over by the forces of evil or compromised in any other way, you won't lose anything valuable. To lock down the network in an emergency, all you have to do now is to physically turn off the power of the guardian machine (assuming this is the only entry point to your local net). This can be very useful if you can't sit down and go though security measures the moment you see a problem, because, say, your boss at the burger grill just does not realize how important that dorm network is and unfeelingly insists you show up on time to flip the meat.
Other functions you might want to isolate on different machines are web- or other servers on your net that people from the Internet can access. You can also have a support machine tend your Linux Terminals (a Terminal Mother) or to burn CDs (a Burner).