Well, building your own depends on exactly what you want to wind up doing and how much space you need and what kind of form factor you want. Along with that is - what do you already have? Do you have a spare case sitting around which can hold 4 or 5 HDD's? Older machine lying around which you can toss a PCIe/PCI card with some sata ports in? The nice thing about the NAS software (and Linux based OS's in general) is that they behave very well even on older, lower spec machines. For something not running a ZFS file system (as in just running straight RAID1, RAID5 or some variation) a Core2Duo with a gig of RAM would be fine. If you want something easy to expand that you can put under a desk somewhere that doesn't utilize expensive parts?
Regardless, here's a basic build which would get you everything you need, not including the drives as that really varies. It'll hold 6 drives however, plus you have some space up top to install an IcyDock hot-swap cage if you want more space or just feel like having hot-swap capabilities. The case does include a PSU, and while I'm not sure if it's the best PSU in the world, you're not building a gaming computer which is going to draw 600 watts, you're powering a Pentium CPU, board, and 4-6 hard drives. Total power draw would be 200w max.
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Pentium G3220 3.0GHz Dual-Core Processor ($56.99 @ SuperBiiz)
Motherboard: Gigabyte GA-B85-HD3 ATX LGA1150 Motherboard ($66.98 @ OutletPC)
Memory: Crucial 4GB (2 x 2GB) DDR3-1600 Memory ($27.99 @ Amazon)
Case: Rosewill I5-397-BK ATX Mini Tower Case w/450W Power Supply ($62.98 @ Newegg)
Total: $214.94
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-09-21 14:32 EDT-0400
Here's a finished build, with a SSD for the OS (just need a 60GB or so SSD) along with 4x2TB Hitachi 7k2000 drives which (according to BackBlaze) have the lowest failure rates of all the drives they monitor. By a big margin.
You could JBOD them for 8TB of total space (no drive failure protection), or RAID5 (single drive failure) them for 6TB, or RAID 10 (two drive failure) them for 4TB of mirrored space.
http://pcpartpicker.com/p/mL6Ppg