Low power, efficient, compact storage server setup

Hardware Build a PC
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This is a consolidation effort as I've got 3 separate PC's with these storage drives dispersed among them and sadly I need them all on atm for access. Hurting my electricity bill since they're all gaming PC's...

The cost isn't too much of a factor. At the very least I'm going for a platinum PSU. I don't think there's anything more efficient than that?

I need a case/mobo combo that holds 6+ sata drives while still being as compact as possible (8+ would be even better). Style/aesthetics are desirable but not necessary. Hot swap is highly desirable or at the very least tool-less.

Everything else I can sort out myself. Thinking AMD, maybe APU if the TDP is low. Definitely looking for the lowest possible power rating overall as this thing will be on 24/7.

Mostly wondering if there's anything special I should be looking for? I'm looking for the -lowest- power utilization possible. Maybe the problem is all my old HDD's? What are the lowest power high capacity storage options ~3-6TB+ ?

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I've considered NAS however as I understand it I don't think I can make individually accessible drives or retain the existing data. Is that correct?

Also a standalone OS would be preferable. Or just throwing it out there as a theoretical possibility but something that makes the drives network accessible and also makes them accessible to a virtual machine running on the same hardware?

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I like to use freenas.
http://pcpartpicker.com/p/CXJdwP
here's my build for a nas.
It's low power-ish efficient if you set it up to be.
It's not very compact but you could make it so with this build by @logan and @wendell