I don't see why you would use 20 machines. I think a good place to start would be RAID 5 using 6 drives so 5 for data and 1 for backup. Which gives 6 machines, assuming your dealing with uncompressed data assuming it's mostly text you can probably use 2 or 3.
How did I screw that up ... woops, let me change it.
I still argue 7 machines though. I mean, sure you could do USB + enclosure or have some more expensive board (with 6 SATA connectors, I don't know how cheap those go). Then you also may need more power, depending on how you use the thing. It's true that fewer machines generally = fewer faults, just as a matter of statistics.
But in reality, in practice, the users will probably have some IBM or SGI solution that is a full-height rack with a bunch of SAS drives or something. I'm sure you've seen those things at trade shows.
But my point here was to try to determine how much it would cost with total baseline OTS hardware.