I would question the benefit of virtualising (or is it written with a z? My spellcheck does not know) your gaming rig. As for the cost: I do not think it will be all that cheaper because you will have to buy more expensive hardware. (Something like: Motherboard with Virtualization support that has a PCIe x16 Slot for the GPU and a 6 core CPU (probably some 6 core Xeon with hyperthreading) that has a ton of SATA ports AND all your memory should be ECC memory.
You won't be buying any less harddrives, any less RAM or be spending any less for the CPU just because you virtualize.
As for power usage: You won't be gaming 24/7 but your NAS will be on 24/7 or at least extended periods of time. If your wall power is shit (Brown outs or Blackouts likely) your UPS has to be bigger if it has to support the beefy hardware (the system will be idling on a higher power draw).
Plus: All the trouble of having a virtualized gaming system (bare metal is unoptimised and problematic enough as it is).
Build a gaming rig with a quad-core CPU and a gaming GPU and put an SSD and a Harddrive in it.
On Redundancy: A flipped bit in a video file is bearable, worst case: an Frame is missing and you have some artefacts for a couple of seconds. Really not a deal breaker. So Really no need for BTRFS or simliar demanding file systems. You can just as well use unRAID with no BTRFS drivepool.
TL;DR: Your problem does not fit the solution you've found :)
I'd recommend a limetech UnRAID solution if you wanted to virtualise some remote-sessions for virtual clients, have a NAS, a DHCP server and a small mail server. But gaming and storage are two use-cases that are somewhat seperate of each other.
So what we need is a build-off of two rigs vs one rig. A gaming system and a NAS system vs the virtualized Gaming NAS!
So my pick would be:
8GB DDR3 RAM
H97/H110 chipset motherboard
the GPU (same as if virtualized)
1TB drive for stuff
PSU (okay PSU, 80+ is enough)
well ventilated case
8GB ECC RAM
2 * 3TB drives for movies and noncritical data (adjust size accordingly)
2* 1TB drive in RAID1 for critical, personal data (adjust size accordingly) + 1TB drive for monthly,cold backup
good, very efficient PSU
NAS: honestly, any linux distro is fine. The RAID 1 will be done in software and shares are SMB shares
vs the unRAIDINATING gaming NAS
X99 motherboard (workstation class)
16-32 Gigabyte ECC DDR4 RAM
Big, very efficient PSU
the GPU (same as above)
All the drives (probably run as one raided drive-pool with BTRFS or ZFS), maybe SSD caching or SSD-RAID for gaming.
Big case with good noise dampening
The virtualized build is maybe a bit overspec'ed. But we do not really know your needs in terms of storage size and gaming. But my educated guestimation would be: Meh, not worth it.
Btw: Thanks for the opportunity to spend my lunchbreak at university.