I suggest you to employ the AMD Eyefinity to serve your purpose. The ''3x1 Landscape Plus 1 Extended'' configuration is exactly what you want.
If you prefer Nvidia, then you will need two GPUs (either SLIing two single GPU cards or use one dual GPU card) to drive three monitors in Surround. Then, you will need an additional graphics card to drive the NEC.
Regarding the graphics power needed, it depends on whether the three monitors are 2560x1600 or 1920x1080.
3x2560x1600 imposes a much higher demand on the graphics power.
I suggest starting with a pair of HD7970s (in Crossfire mode).
For 2560x1600 monitors, there are not many options. The general consensus is Dell U3011 or HP ZR30W.
For 1920x1080 monitors, there are many choices. And the budget makes the decision.
Regarding the max length of DVI cable, IIRC, the spec says 5 metres (15 feet). I suppose 20-25 feet is still safe without problem. After that, you may need a signal booster.