If you want to buy a pre built solution, you're looking for HP MediaSmart. See:
http://www.hp.com/united-states/campaigns/mediasmart-server/...Size wise, it's small (photo: http://www.ehomeupgrade.com/wp-content/uploads/hp_mediasmart...). Cost wise they're relatively cheap (considering it comes with enclosure, cpu, motherboard, hard drives, etc), I've seen them for ~$300-350.
It uses Windows Home Server plus their own custom add-ins. They're nice. You get everything I mentioned before, except this is pre built. They have things like integration with Tivo. I decided to build my own since I had spare parts lying around, otherwise I would have bought one of the MediaSmart machines.
Also, when you say something with "more media capabilities", it is doubtful you will be able to surpass a WHS-based system. This is because a system like MediaSmart, out of the box, will stream everything to any PC, any mobile device, any windows media center, etc. They've built it for streaming media, and all kinds of ways to access the content are already in the ecosystem. They have even included a silverlight/flash based streamer if you decide to only use a browser (they transcode on the fly then stream it to your browser). Devices (eg. xbox 360) and even entire OS's are designed to work with WHS (Windows XP, Vista, Windows 7).
One more thing: the WHS and MediaSmart communities are great. Many websites/forums discussing ways to use it, how to optimally set up your home, issues you'll encounter (and resolutions), etc. (http://www.wegotserved.com, http://www.mswhs.com, http://homeservershow.com, http://www.whsaddins.com, http://www.homeserverhacks.com, http://www.mediasmartserver.net, to name a few)
If you're looking to start out with your first home server/theater, the community welcomes you.