I've never even seen a Zune (and presume they aren't that popular for a good reason), but I'm happy to recommend an iPod. I bought a refurbished 20GB one, 4th generation before the first colour displays, on eBay a couple of years ago and it's still going strong. Even the battery life is decent, however I should add that I treat it comparably well.
Depending on the model you get, you'll either have an iPhone-like interface or one with a "click wheel". Mine's got the latter, simpler one, and I find it to be close to perfect. Five buttons (apart from the hold switch) and the wheel are all you need for the rather simple task of choosing the music you want to listen to. Word of warning: if you plan on using your portable media player while running (or on rollercoasters, very bad roads etc.), don't get one with a HDD but one with flash memory.
As for iTunes, I guess it's a love/hate issue. I've configured mine so that it'll copy any audio CD I put in the drive and eject it, so copying my entire CD collection was a matter of putting the disks in, occasionally choosing between more than one available track list, putting the discs back into their cases and creating playlists by drag-and-drop. It was infinitely better than the pain of doing the same with Windows Media Player. In short, I organised files in WMP and organised music in iTunes.
The iTunes Music Store (ITMS) however got somewhat worse with the latest update, they ditched the shopping cart for no apparent reason and changed the layout for the worse. But it's still 100% integrated into iTunes, so it's retained that "it just works" feel. DRM is, fortunately, a thing of the past so you can use your files the way you want. Even so, I never really had a problem with it since I only ever used them on my iPod. As for pricing, I believe that the ITMS is in many cases more expensive than some other sources. But a) you said you didn't want to buy a lot of music and b) AFAIK, you can use files you bought elsewhere in iTunes.
Finally, iTunes has a variety of radio stations for you to choose from and you can add streams to the library. Bandwidths vary depending on the station.
sosumi