I think you're looking directly at a small Windows Home Server (2) build, and it doesn't have to be very powerful at all. XBMC is an option if you're just streaming media since you don't have to manually mount an ISO and it just does it for you; it's $50 less (free) too. You'll want to focus more on the network vise the computer IMO.
What I use is an Asus iTX, little Intel G1610 Celly, 8G of Mushkin 1333 (was cheaper than it is now), and then a crap load of WD red drives in a Fractal Designs shoe box. The network is (was, we moved and I haven't set it back up since I want to move again) based on a managed 16-port gigabit switch. I added some outlets in the upper hall closet, placed the iTX up there, a small UPS, the switch, the modem, and then a 4-port Asus Black Night wireless router is right outside the cabinet on the wall. I'm not sure what they're called technically right now, but I bought a TP-Link patch panel to mount in the closet and that's the only part you run the CAT 6e out from to the individual plugs throughout the house. Once all that is wired to the patch panel, you only need little 15" home-made patch cables to jumper from the switch and it's just more clean in the closet and better to manage IMO.
I like the idea of a digital home, but I do NOT like that it's being focused on wireless a little bit too much. No, wait...too much indeed. I know it takes work, but a good wired network is painless once it's set up and all the hard work is done building it. Mine is a bit of a complicated plan, but it's abilities are really endless. Want a home surveillance system some day? Just plug it in to the already built system, and most switches have ports just for this. If I'm going through the trouble or running fast hardwires, might as well get the whole house for more techy stuff we may not realize we want currently.