Certainly not cheapest, but definately really easy - you can look at Synology or Drobo (and other NAS vendors) for out of the box experience. I'm very happy with my Synology and definately recommend it.
Buy the biggest case you can afford with as many drive bays as possible, fill it up with 3 or 4TB drives, slap in a $30 celeron and $70 B75 board and install a decent server OS (I'd recommend Debian). Set it up (Gigabit preferred) and you are good to go. I'd avoid a NAS, unless you buy one that has everything you could possible need, they are not expandable at all.
That Extreme Series intel MB was an opportunistic purchase and has 4x SATA3+4x SATA2 ports. Adding a Highpoint RR2320 card gives this server 16 ports capability. I will add a 6x 2.5in in a single 5.25in bay housing giving this box 14 HDD capability, 8x 3.5in+6x 2.5in. The OS SSD will just be wedged somewhere in the case. A multi-card reader occupies the 2nd 5.25in slot.
The Seasonic PSU cables are too short so 24pin-24pin, 4pin 12V cable extensions were added. Fractal Design fan control was too primitive. Rear and top fans were replaced with Rosewill 140mm PWM fans. Original fans were moved to the front and connected to a thermistor equipped fan controller.