Or an android tv supported by a privacy respecting custom rom.
I don’t know if the NUCs have IR receivers OOTB, which you will need to use a standard remote. I know the raspberries have them.
For best compatibility with NUCs I would just google for which distro to use. You’re definitely not the first person to use them as media PC. I use Nobara on my Beelink and everything worked OOTB, but that’s different hardware. Once you have a distro running you have all the options of a PC to run Plex, Firefox, Spotify, etc…