No computer with fans is silent. Quiet, yes.
For good research on quiet computing, go to www.silentpcreview.com
You can run 3 1080P monitors off of the integrated graphics of a 4770 and a appropriate motherboard..
Monitors do not attach via usb ports.
You may want a B85 motherboard which is cheaper since you will not be overclocking.
The noctua NH-D14 is probably overkill, but there is nothing better or quieter.
One of the other noctua tower type coolers with a 140mm fan would do just as well.
Fans cause noise. You do need need extra cooling. I would try the stock 140mm fans first.
Just one 140mm as intake is sufficient.
No value in adding more.
The Samsung ssd is fine.
You might buy a larger ssd and ditch the hard drive entirely.
Samsung EVO is cheaper and will perform equally well.
For a trading sustem, consider a single 4k monitor.
seiki has a 39" and 50" unit that looks stunning. I saw one at compusa.
You could fit the equivalent of 4 1080P monitors on one.
The advantage is that you could resize your chart windows and locate them appropriately.
I think the haswell chipset will support 4k via hdmi.
You only need a minimal psu. 400w would be all you need.
Buy a gold rated Seasonic unit. The fan will not run at all because it is so efficient.
Use an external usb hard drive for backup.