When I attempted Plex, it was a HOG! Would not run on 918 or Nvidia Shield correctly. Went with Kodi and never looked back. But I would recommend i7 Nuc for future proofing. I run Proxmox on mine and run HA + Windows 10 and a few other vm’s when I need them.
It runs good on the synology when using direct play (except huge 4k hdr files buffer sometimes).
But transcoding is not good.
I consider jellyfin since it can use the hardware acceleration on Intel CPUs. But my TV doesn’t have a client app. So I might need to use something like the new chrome cast for that.
I run HAOS on an i3 NUC and Plex on an i7 NUC. I am not a fan of multipurposing - I like to keep my installs simple. (For example, if my Plex NUC goes down, all that is offline is my Plex- not everything). I actually have four NUCs. The third is my general purpose Ubuntu machine, an I5 running Mediawiki plus other experimental stuff. I have an i3 that is still on the bench but it will be running as an NAS and a collection point for my backups.
BTW- Only my first NUC was purchased new. All of the others are from eBay and cost less than $100 plus memory and SSD.
My HA system is a NUC i3. Had considered a NUC i7 for Blue Iris, went for a Dell OptiPlex Micro system i7. It has an active cooling fan for the processor, which some NUC systems may not.
Thought I would add my 2 cents …
I started with an older NUC back around 2018 and it had an Intel® Celeron® processor N2820. I ran HA in a Python venv and even ran several other processes too (MQTT, ZWaveJS-UI, etc).
I recently moved to a NUC marketed by the name “Tiger Canyon” which uses an 11th generation i5. Its pricey, but I wanted to run HA in an Ubuntu hosted QEMU/KVM setup and still have the ability to do other things.