You're still gonna need a decent system, particularly if you want it to last and will be using it all day everyday.
You'll probably want at least an Intel Core i5 or i7, Minimum 4GB of RAM if not 8GB, RAID harddrive solution for data (I would have a single non-RAID drive for Windows and then 3 or 4 drives in RAID for data).
Then to run your 3 monitors, you have 3 options:
1) install 2 graphics cards and run a bit of software called SoftTH which will span your desktop across the 3 monitors
2) buy a proper Triple/Quad Head graphics card like this:
Matrox M91383) to run a decent graphics card into the
Matrox TripleHead2Go, which takes a single screen input and splits it properly for 3 screens.
Matrox have been making multi-monitor video cards for years and are rock solid, trusted by business and the media industry. They're not cheap and they're not going to set the gaming world alight, but they're very good at what they do.