Seen as you already have some of the parts on hand, build a server as it will allow for a lot more functionality than a NAS would, afterall it is a full-fledged computer. FreeNAS, WHS, Windows 7 or 8 would all work well for your intended purposes, however their may be a slight learning curve to set up depending upon what environment you are familiar with. A Windows environment can accomodate iTunes wonderfully (which I also use to organize my media to stream to an Apple TV), however I cannot personally recommend Windows 8 and it's Storage Spaces feature as I have yet to upgrade my media server to that OS.
There happens to be a great website that focuses on WHS & NAS:
We Got Served