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How much capacity do you want?
I'd setup one of the old laptops with an external drive bay like this:
Amazon Media Sonic 4 bay
Then another one, with your backup, that you keep at someone else's house.
Check out Blackblaze for backup as well.
Not the same brand, but I've been using this box for about a year now in an unraid server. Yes it gets hot, so I opened it up and stuck a fan in front of it.
I would get something like this and keep everything you're doing the same:
> NUC can hold 2 drives
2 m.2 drives.
You can use up to 3 USB3.0 drives with it, or you can get a DAS unit like this:
Also, you are indeed overspending. This would be sufficient with a Plex Pass to enable hardware transcoding:
Intel NUC NUC7PJYH
You could use FreeNAS or UnRAID as an OS if you'd like it to be storage-focused.
Here is the same thing for cheaper.
I use mediasonic drive enclosures. Like this one Mediasonic HF2-SU3S2 4 Bay 3.5” SATA Hard Drive Enclosure – USB 3.0 & eSATA Support 16TB – (Renewed) https://www.amazon.com/dp/B072HW3C4C/ref=cm_sw_r_cp_api_fabt1_BsBWFb23WXN44
A $100 laptop off Craigslist and an external drive enclosure would get you up and running for about $200 total.
I think you'd have to connect the blu-ray drive to an actual computer. It doesn't have to be a new one, it can be a used one. Serverbuilds.net maintains a list of ebay links for computers that have Intel's QuickSync encoding hardware, which is handy if you decide to pay for Plex Pass.
Having the server machine also means that you can use a Direct-Attached Storage unit instead of a NAS, which should save you a little money.
> Tangentially, is it possible to pull selected movies from the server onto the iPad so I can take some movies on road trips?
Yes indeed! This is one of the more popular features of Plex Pass, but from what I understand, it doesn't work for everyone all the time. I usually pull my music straight from my server to my phone using the file browser and wifi.
Here's a 4 bay USB 3.0 enclosure from Amazon: https://www.amazon.com/dp/B072HW3C4C/ref=cm_sw_r_cp_apa_i_LyxwBb86E17C4
I can verify this model works with Windows/DrivePool/Plex.