From reading your question and the answers so far, I'd like to clarify some terms in hopes to help you find what will help you best. Having a hard-drive manufacturer say their drive is Time Machine ready simply means that it is already formatted for the Mac. But you can always bring any external drive and format it for the Mac using Disk Utility. Of course, doing this will erase the drive, so keep that in mind.
Once you have your hard drive, then the next thing to clarify in the discussion is Time Machine Vs. Time Capsule. Time Machine is a Mac OS X feature that will back up your data in the background. However, this feature only works with a hard drive physically attached to your mac. As far as I know, it will not work over a network.
On the other hand, Apple sells a product called the Time Capsule (do not confuse this with Time Machine). The Time Capsule is a wireless network hard drive that Time Machine actually supports. Adding a Time Capsule to your network would be the only official way to use Time Machine over the network.
Finally, regardless of whether or not you're using a Time Capsule: When you use Time Machine on a hard drive, you can continue to use the remaining space on the hard drive for storing whatever you want (like your iTunes library in your example). In other words, using Time Machine will not make use of this drive exclusive to Time Machine. The only thing to keep in mind is that Time Machine will create a folder at the root of the drive where it will keep its backup sets. Leave that folder alone and you should be fine. :)
My current set up consists of a 1 TB Western Digital hard drive attached over USB and backing up using Time Machine. Time Machine will create sets for each one of the last 24 hours, each one of the last 30 days, and each month until it runs out of space. In order to make the best use of the drive, and this is a tip I wanted to share with you, I have configured Time Machine via System Preferences to ignore the Downloads folder and my iTunes Podcasts folder, which have tons of data that I do not need to back up.
You may also want to consider looking at a Pogoplug. I do not own one (yet), but it looks like a compelling alternative to create a shared media hard drive on my local network.
Hope this helps sort things out.
Update: As it was pointed out on this thread, there is a way to get Time Machine to work over a network. It involves modifying preferences files via the terminal and while it is not a difficult process, it is evidently not an officially supported method to use Time Machine--otherwise, the System Preferences UI would allow you to select network drives other than Time Capsules. The name of the configuration value that must be modified, "UnsupportedNetworkVolumes", hints at this as well.
So while the answer to the question "Is it possible?" seems to be yes, my advice for the tweak suggested on this thread is to use it at your own risk. I can't help to think that there could be a technical reason why Apple has not allowed network drives to be used for Time Machine out-of-the-box. Perhaps they haven't obtained optimal results. Perhaps a Time Capsule is better designed for working with Mac OS X and the way Time Machine itself it designed. Or... and this is also a possibility, Apple is only blocking network drives to sell more Time Capsules.
In any event, if you experience excellent performance with Time Machine using an officially unsupported network drive, please post to this thread and let us know how it works. Good luck.