You could look at something like P182 (because it's quiet) or Antec 300 (cheap).
I'd recommend WD1001FALS disks.
A GA-MA780G-UD3H has RAID 0/1/10 and the best integrated video chipset available. You wouldn't need any video card at all.
Pick an AM2+ CPU for it (e.g. Athlon 64 X2 7750 Kuma 2.7GHz $60 at Newegg or AMD Phenom II X3 720 2.8GHz for $135).
If you want RAID 10 (or 1+0, to be exact) and 3GB of storage, you'd need 6 1TB disks. That is, 3 pairs of 2 disks. Each pair has a primary disk and a mirror for it, and the pairs are striped together for speed.
You'd need an IDE DVD burner because the MB only has 6 SATA ports.
The cost would be around 60 (case)+660 (hard drives) + 90 (MB) + 135 (CPU) + 50 (RAM) + 30 (DVD).
Excellent point. Maybe something like NZXT Tempest, or HAF 932?
Isn't that 6 HDDs, for 3 TB of storage with 1TB drives? Just trying to get my head around this RAID type. If I understand it correctly, you can do this with 4 Seagate 1.5 TB drives too, also for a total of 3TB, but Seagate is less reliable these days.