I spent about half your budge for a...
$168 AMD x2 4200 CPU/PC Chips A13G+ Socket AM2 Motherboard /2 GB DDR2/667MHZ Combo (I don't recommend using this brand motherboard)http://cgi.ebay.com/AMD-Athlon-X2-4200-CPU-2GB-DDR2-RAM-Motherboard-Combo_W0QQitemZ130202983274QQihZ003QQcategoryZ149173QQssPageNameZWDVWQQrdZ1QQcmdZViewItem
$55 Nvidia 6800 PCI-E Video (this video card does not give me video out the vga port during the initial AVWizard I had to use the number key method.)http://cgi.ebay.com/Dell-NVidia-GeForce-6800-PCI-e-x16-256MB-DVI-VGA-MG229_W0QQitemZ220206298646QQihZ012QQcategoryZ40161QQrdZ1QQssPageNameZWD1VQQ_trksidZp1638.m118.l1247QQcmdZViewItem
$45 PVR-150MCE TV Tuner Card (worked flawlessly)http://cgi.ebay.com/Hauppauge-WinTV-PVR-150-MCE-TV-Tuner-FM-Windows-Linux_W0QQitemZ330216949182QQihZ014QQcategoryZ3761QQssPageNameZWDVWQQrdZ1QQcmdZViewItem
$65 Gyration GO MOUSE for my remote. (worked flawlessly)http://cgi.ebay.com/GYRATION-GO-2-4-OPTICAL-AIR-MOUSE-UP-TO-30FT-RETAIL_W0QQitemZ380001943198QQihZ025QQcategoryZ15388QQssPageNameZWDVWQQrdZ1QQcmdZViewItem
$38 80GB SATA Drive (duh)http://cgi.ebay.com/Western-Digital-80GB-WD800JD-SATA-2-Hard-Drive-80-GB-WD_W0QQitemZ260215698668QQihZ016QQcategoryZ64459QQssPageNameZWDVWQQrdZ1QQcmdZViewItem
$3 DVI to HDMI cable (I have an lcd hdtv so I needed hd cable)http://cgi.ebay.com/Gold-Plated-10-foot-HDMI-to-DVI-For-HDTV-Premium-Cable_W0QQitemZ270216601454QQihZ017QQcategoryZ64631QQssPageNameZWDVWQQrdZ1QQcmdZViewItem
$12 SPDIF output header for motherboard (connector can be re-arranged to fit any spdif header on any motherboard)http://cgi.ebay.com/Gigabyte-Motherboard-Coax-SPDIF-In-out-Audio-Cable_W0QQitemZ330216434925QQihZ014QQcategoryZ1244QQssPageNameZWDVWQQrdZ1QQcmdZViewItem
$35 Case w/ 600watt powersupply (duh)
Total combined shipping was around $60.
My total came to just under $500 usd... This is the exact system i'm running flawlessly. Actually it seems a little too much for it, until I put about 3 MD's on it before it starts to lag behind.
Whatever you go with, i'd reccommend using hardware that is known to work flawlessly with linuxmce by using this as a guide http://wiki.linuxmce.org/index.php/Category:Hardware
. Trust me, it's easier to use whats been confirmed to work than try to re-invent the wheel. Use that link as a guide and you should be fine in whatever you choose to go with.
Also, you mention streaming, keep in mind, for the TV Tuner, you can only stream the currently tuned in channel simultaneously to all MD's, or watch tv on just one md at a time. You won't, for example, be able to watch channel 22 in one room, and 49 in the other. To do this, you'd need a dual tuner card, which is the PVR 350 I believe (not sure off hand)... and even then, that only allows you to either, watch one show while recording another, or have only 2 rooms be able to watch different channels. You would respectively need one tuner per room you want independent TV in. Streaming anything else is free ball game though...
For media directors, I personally use old thrown away laptops. They range from 1ghz with 512mb of ram to 2.8ghz with 1gb of ram... they all work fine for me in UI1 mode. I have 2 that work great in UI2 mode (ATI Mobility Radeon 7500 cards that work with ui2). With media directors, you can get creative, since the MD can boot from the network you will only need a barebone computer system with a network card.