In my bedroom I have a US$200 EeePC netbook running XBMC (XBox Media Center, http://xbmc.org/
). This covers all of your requirements, with a couple of caveats:
HD - I've got a little EeePC 900A, and its processor can only get as far as 720p. A different device might get you all the way to 1080, I don't know.
Stream from web - In principle it does this, and I use it on the XBox in my family room. But the Linux distro of XBMC doesn't come with the scripts that accomplish it. I'm not sure if you can just steal the same scripts from the XBox or Windows distributions.
Storage - obviously on a netbook, storage is limited. You might get away with a moderately sized music collection, but you're not going to have on-board storage for movies. For that you'd have to supplement it with something external. In my house I have a NAS for this (a D-Link DNS-321 with two 1TB drives in a mirrored RAID array).