@ danzg
First keeping this real... You wanted to build a HOME NAS, not a NAS for business use so lets keep that in mind. Will you ever truly "need" more than four 2TB drives? If you really think you will expand within the next 3 years, buy a slightly larger power supply or maybe you will replace the 4 drives with new 4TB drives, after all the four drives you are getting today will likely be at the edge of their life in 3 years.
Your RAM selection is off, you are buying 3 sticks of 2GB but did you read the users manual to see if this was possible. I recommend buying either 2 sticks of 2GB (4GB total) or 4 sticks of 2GB (8GB total). The users manual doesn't say it works with three sticks, it only talks about 2 or 4 because this is a dual channel memory setup. I'm running 4GB and she works great. You can keep the extra as a replacement part or you could plug it in a try it out. Ether way run MemTest on it over night to ensure the RAM is good. Remember to plug the RAM into the proper sockets (read the instructions)
In my opinion the system you picked is sound with one serious exception, the power supply. You are looking to purchase a bargain brand cheap power supply that I could only find one review on which stated it was a an okay entry level power supply. Even that review didn't get into any details of what they tested. $70 is not enough to spend on a quality power supply. The only plus I could see about it was it said the magic words "Active PFC" which is absolutely the right direction. Maybe someone could tell you there are some reviews here and it's a great power supply but until you have read a comprehensive test of that power supply, how do you know the 12 volt rails are solid at 80% capacity (example).
I've been building my own home computers since 1980, yes I tell no lies, and some were soldering the components to the boards. Those were the fun learning days.
For the 80Plus to give you maximum performance you need to by the right power supply for the power used. Your system requirements don't look severe unless you add a gaming graphics card to it or a high end CPU. You should calculate out your total watts and be at around 80% capacity of the power supply to give you some expanding room.
Here are my recommendations based on your system.
Running 4 drives
Fanless @ 400 Watts
http://www.newegg.com/Product/Product.aspx?Item=N82E16817151097
Running 8 drives
Fan @ 500 Watts
http://www.newegg.com/Product/Product.aspx?Item=N82E16817379005
Fan @ 560 Watts
http://www.newegg.com/Product/Product.aspx?Item=N82E16817151098
This one is overkill for your current system but it's a high quality power supply. This company NZXT use to make a 450W power supply but I haven't seen one in a while.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817116011
Now since you wanted a quiet system, I noticed you never mentioned a CPU heatsink. It's going to be loud if you use the stock fan (if you bought a boxed CPU), no box, no fan. First, you need Arctic Silver 5 or similar product and it really does make a difference what heatsink compound you use and how you put it on (just a thin layer and use a utility knif blade or the like to spread it thin, paper thin). A great quality heatsink will come with quality compound so check that out first. Buy as large a heatsink as you can to fit inside the case. You want the largest fan possible which then the fan turns slower and reduces noise. Both my normal computer and NAS are virtually silent. My NAS sits in front of my feet with the cover off and I cannot hear a peep out of it unless the drives are spinning up. I can't even hear then access because I bough quiet drives, not because I'm deaf.
Since the case you picked out is 8" wide (good choice by the way) you can fit almost any heatsink in there. Here is my recommendation but you should ensure it is compatible with your motherboard, but I suspect it is. Don't let the first photo fool you, it does come with the fan. And I have two of these (the intel version) in my systems. Love Them!
http://www.newegg.com/Product/Product.aspx?Item=N82E16835233003
And I assume you have a CD-R drive to load the image the first go around and any time in the future. Well that should do for now.
Sorry I didn't read your message sooner.
-Mark