Look into the Lian-Li PC-101 or V1100. Both are extremely quiet. I tend to find the PC-101 has slightly better cooling capabilities and its the cheaper of the 2. This is because the 101 has vents on the side of the door, while the V1100 has vents hidden underneath and the door is sealed. However the V1100 is quieter by a pinch. Overall I recommend the PC-101 though.
You will likely need slightly longer SATA cables than come with your mobo if you use either though. Also avoid ultra-long and modular power supply's with either. As they HDD/PSU chamber is only really long enough for a normal PS. I found the Seasonic S12 Energy Plus PSU's are a perfect fit and very good quality + power for a build like this.
Also If you really want to stay cool, take a PC-101 and add a
3x5.25 Inch Bay to 120MM Fan Adapter fan adapter. With this the case is is amazingly quiet and cool. Since it vents the air in through the sides of the door, and it has a filter on it. Plus the HDD chamber has a dedicated 120mm fan for the 6 Hard drives.