Leon,
Is it going to be a unix (of some type) or windows server? I assume you have somebody who is competant to manage the server.
Are you looking to build a fast computer that is pressed made into a server (1 or 2 thousand) or are you looking to make a real server (scsi raid, redundant power supplies, etc) (several thousand, minimum)
What domains do you own?
Are you running your own DNS server, or taking advantage of the hosting companies?
For those people who don't want to spend the money to buy a domain, but don't like any of the ones that they provide, you can also use a subdomain of any of these:
http://www.dyndns.org/services/dyndns/domains.html for free.
Aaron, it would depend on whether your school's administrator would modify his DNS server to point that domain at the new server. Technically it can be done, be they may not want to do it for you.