You'll be looking at Windows 2003 one of the Server versions and depending on exactly how many computers are involved it will depend on which one you'll actually need. But it is a relatively simple upgrade as all you need do is install the Server and set the Domain Name to the existing "WorkGroup" Name. Depending on which version you actually get you may have to set a max number of clients on the Windows 2003 install but even then it's not all that hard.
That will get you up and running but then you'll need to think about exactly what else the Server will be doing and what security you will need on it as well. I take it that all the computers are connected to the internet so you'll need some form of mailing program as well as AV and a Firewall at the very least. MS make a reasonable thing in ISA so that may be worth a look see as well.
Then you will have to decide what will be stored on the server, what will be shared and what protocols you will need to put in place.
That way you can keep the Y2K desktops and have a somewhat easy transisition to a Server network although you'll find a lot of ways to make it far more secure with time and a lot of effort.
Or you could go the "Open Source" route and just dump MS all together with Samba and one form of Linux you could do exactly the same thing but if you have no experience with Linux it will be a bit more work although a lot more secure.
However if you already know Windows fairly well it will not be a hard step.
Col