HDMI sends video and sound, im not sure but i think its upto 7.1 audio max, so would be fine.
Im pretty much out of date with prices/hardware at the moment, but from reading your post the idea of a solid state drive crossed my mind. Im not sure how fast they are - or appropriate, but im fairly sure theyre not that expensive if you just want to run an OS off it. They should be fairly fast and quieter than a normal hdd. Also depends if youre going to have the data library on the media pc or stream it over the network.
Probably the main thing you want is for it to be quiet, the lower end new graphics cards support HDTV pretty well, but because theyre shit for gaming they dont require fans etc. Combine with a cpu you can passively cool. Or just put the whole thing in a different room, but thats not ideal.
Havent done this myself so cant really say anymore, should be as simple as making a quiet pc with media centre/remote control.
