If you're going to be doing transcoding for remote users at lower bitrates, quicksync is still better than AMF, so I'd vote Team Intel.
If you're not, then buy whatever meets your power envelope desires and price point.
For Intel, anything 8th gen or newer should be able to natively do anything you need in Quicksync, so you don't need to head to Amazon and buy something new, unless you really want to.
Also, I'd consider hardware that has enough SATA ports for the number of drives you want so that you can avoid dealing with a HBA card: they inflate the power envelope of the system (if power usage is something you're concerned with), and even in IT mode, I've found them to be annoyingly goofy at times and am MUCH happier just using integrated SATA stuff.
Yeah, it doesn't sound like you're transcoding in a way that'll show any particular benefit from Quicksync over AMF or anything else. My 'it's better' use case would be something like streaming to a cell phone at 3-5mbps, and not something local or just making a file to save on your device.
That's what my build is: 128gb of Corsair whatever on a 10850k. I'm sure there's been some silent corruption somewhere in some video file or whatever, but, honestly, I don't care about the data enough to even bother with RAID, let alone ECC.
I will say, though, if you're going to delve into something like ZFS, you should probably consider ECC since there are a lot more 'well shits' that can happen than what I'm doing (mergerfs + snapraid).
A $30 or whatever they are kill-a-watt plus something like s-tui running on the NAS itself to watch what the CPU is doing in terms of power states and usage. I've got a 8-drive i9-10850k under 60w at "idle" which is not super low power, but it's low enough that the cost of hardware to improve on it even a little bit (and it'd be a very little bit) has a ROI period of longer than I'd expect the hardware to last.