Well I'd like to power down most if not all the computers when not in use. I stream stuff using network shares to various TV's around the house at varying times. In doing more research on the Raspberry Pi I came across a couple of articles where the author built a dual disk system, main drive held content and the second drive was set to back up any changes at 5AM. Might be serviceable for me.
If all of those PCs are energy hogs, I can understand that. But if just one of them draws fairly low power, the simplest and cheapest path is to simply use it with a drive. If lowest energy consumption in your server is the #1 priority, then a little ARM based system makes sense.
Be careful how you "backup" your files. An automated backup that is only doing a mirroring of the content drive is no better than RAID.
Other option I have not researched too much yet would be to store all my content on a WD or Seagate 4T Usb drive and simply plug it into my Asus RT-AC87U router. Downside is no backup.
It could be backed up across the network to a drive inside or attached to one of the other computers. The initial backup of several terabytes of data may take some time, but after that incremental or differential backups shouldn't take much time. Media files tend to change very little, and most people only add a limited number of new files each month, so it's typically not something that needs to be backed up daily. I backup mine just once a month.
I do not do any transcoding at this point. I avoid DNLA media server in favor of SAMBA shares. If I was doing remote viewing odds are that would be involved.
Yeah, I was going to say that another consideration is processing power, but apparently it's not a concern for you. Personally, at a minimum, I'd want a server that could better run some media server software and have the ability to house additional hard drives. That can be done fairly inexpensively with a small mini-ITX system with an Atom or Celeron processor, in a small case that can house a few hard drives. With the drives spun down and the CPU in power saving mode due to inactivity, it would draw very little power.
After file serving, the second most important task for my network server is hosting backups of all the PCs on my network. Maybe something to consider when thinking about drive capacity.