You don't need to keep media center running on the server machine, as the library server will run in the background, allowing everyone to connect to it. You'll see the icon in the notification area, and clicking on that icon will give you the option to open Media Center (which will let you see the local version), or close, which will close the server altogether. Make sure you have "run media server at startup" set in options on that machine, so that it always starts up when the machine does, so you don't forget to start it manually.
I have no idea about the UNC stuff, sorry. i just map Music to M: on all my machines, and that works for me just fine. (Photos to P:, etc.)
I can't say what the advantages or disadvantages are of the UNC setup he describes, but the mapping was easy for me to understand and setup, and has worked fine for me for years.
I'm sure jmone will give some more input on the UNC stuff for you, i just wanted to help with the server part, and let you know that mapping works fine also.
have fun