Regardless if you use a NUC or NAS, I would recommend focusing on the processor. Make sure it can can handle the type of codec that you’re wanting to transcode to and from (hevc, avc) on the transcoder device. Intel QSV is also pretty nice if your chip supports it and you don’t care too much about quality.
Here’s my (semi) educated opinion: Get a NAS just for storage and retrieval. Get a NUC with a modern chip and run your apps and transcoding on it. I have this in my lab and it allows me to upgrade in the future depending on what my needs are. If I need more processor power, I get a new NUC. If I need more storage, I can add an expansion device and/or replace the NAS completely.
If you combine the storage and transcoding into a single device on the NAS, you’re locked in if your needs change and you will need to start looking at more expensive HCI options.
I don’t think you really need a 10gb network, unless you’re pulling down 4k and 8k video files or if you have over 10 users connecting at a time.
At idle, power consumption of the NUC is very low–about 5 watts. At load, it’s about 100 watts.