Sorry if I'm not going into detail as to why some of the thing I will recommend are good, its quite late where I am and my bed is beckoning. I will likely get back to you tomorrow sometime with a bit more info.
From that, seems you only need a computational machine that has basic graphics capability to drive a few monitors (Three? More?)
The core of the rig would be.
An i7 3770, B75/H77 mobo, 16GB of 1600Mhz RAM, good quality 500W PSU, a hefty sized SSD (depending on storage needs) and something like a HD7750 to power all the monitors. Probably a sleek minimalist case as well.
The i7 is for the hyperthreading, which helps in number crunching loads.
B75/H77 mobo because you dont need enthusiast featuers on this kind of rig.
16GB of RAM to help with the number crunching.
PSU doesnt have to be all that great, this machine will be fairly low power use so no need for a big supply.
The large SSD (256GB probably) as then you could easily fit the OS, any programs and raw and refined data on there. Though if you do need more storage than that, getting an additional HDD is probably the way to go.
The 7750 is going to be needed as integrated graphics cant support more than two monitors, and is fairly weak compared to a low end card like the 7750.
Estimated cost of a rig like this: $1000-1100 not including the monitors.