Common theme seems to be to take your Raspberry Pi and make a media center out of it. This light article talks about it and the additional “stuff” you need. I would put the total cost closer to $160 (author sais $100, but used some parts on hand). At that price, it would be eaiser to convert an old atom system (laptop perhaps). But may not be as quiet or low powered as the RPi. Oh and I don’t think I would add such a large drive (physical size) to something so small either.
http://www.makeuseof.com/tag/build-a-raspberry-pi-media-center/