A NAS is really flexible - especially for storing Music / Video and streaming via things like PLEX / VLC etc.
My own preference is to use a cheap "Cube" type server running Linux rather than a "dedicated NAS" as it's open source and hugely more flexible. A cheap "Cube type microserver" doesn't need mega power CPU but is built to run 24 hrs a day 7 days a week on lowish power and is much more robust and reliable than some of the so called dedicated NAS systems.
As people have also said NAS needs to have backup as well -- one or two of the small passport type self powered 4 TB USB 3 drives are excellent for this -- the new 4TB HDD's are reliable, fast and consume minimal power.
Either will work, but I think that two 8TB drives would be better.
Make sure to set them in a RAID 1 configuration so that they constantly mirror each other.
Putting them in your PC enables you to use the personal version of Carbonite with unlimited storage for a something like $60/year. I have over 1TB backed up with them no problem.
I apparently succesfully installed two 8tb hdds in two mirror way. Hopefully none had a fall in the postal transport and will last long :-)
The new small self powered 4TB external USB 3 passport drives are excellent for backing up a NAS. These are quite cheap and you don't need (in fact you shouldn't) keep them on line after your backup.
Also remember that when backing up you should always have at least 2 different sets of media since devices can (fortunately not often) go defective.
If you use Linux systems for your NAS - then I'd recommend formatting the backup drives with EXT4.
Unlike most here I run RAID 0 on the NAS (doubles the speed and capacity of the HDD's (2 X 3 TB and 2 X 4TB as an array of 2 drives 6 and 8 TB). Since I'm backing up the NAS I can afford the risk with RAID 0 - it's worth it in performance and capacity gain - especially if you are also running video servers on these that need transcoding from time to time.
I have 2 X HP ProLiant Gen 8 Cube Microservers running CENTOS 7 -- these HP Microservers are brilliant --cheap, quiet, built for running 24 hours a day 7 days a week.
If you connect the DVD connector (on these HP micro servers) (you don't need a DVD on a server) to an SSD and create a single RAID 0 array on the SSD you can BOOT from the SSD leaving the 4 bays available as your data area. It sounds bonkers to create a RAID 0 array of 1 Disk - but that's the only way to boot from the DVD bay (SSD) - otherwise you have to boot from one of the HDD bays if you use RAID. It's better to keep the OS separate.
If you backup your NAS I can't see the advantage of running RAID 1 - since you already have the backup so why waste capacity and speed.
Sorry - but just my take on it.
Of course everybody has their own backup strategies IMO having adequate backup for the NAS boxes obviates the need for RAID 1.
Even with RAID 1 if you rely on a single box you can still get hosed if it fails seriously. That's why external backup is my preferred way of backing up. RAID 1 is only needed in "Mission Critical" stuff where you can only afford to be "down" for a minimum amount of time. I don't believe Home users come into this category generally. !!!