The NUC way will be very nice, i can confirm. Switched to a NUC for Plex along with a Synology as NAS. Both conntected with an own gigabit ethernet switch. There was no issue in the last 4 years.
Regarding I7, I9, 10th, 11th gen NUC, it may depend on the amount of concurrent users you want to serve. But maybe all the mentions here are a bit overscaled.
For example, a 8th gen I3 NUC can handle 5-6 concurrent fullHD x264 and x265 transcodings without any hassle, even 2 4K HVEC transcodes were no problem here. In fact the only thing needed is the Intel QuickSyncVideo engine in the video hardware, I have not seen the I3 going higher than 25% load.
If this suits you needs, you could get an older gen NUC for maybe 250 bucks.
But sure, a beefy fresh NUC will be nice.