keep in mind that if you want to transcode with Plex, you'll need to subscribe to their Plex Pass... unlike Jellyfin which is completely free

I would recommend checking out Jellyfin (an open-source Plex alternative) to see if it meets your needs, as it's actually free as opposed to Plex.

I would say that the Intel Core is probably a better choice, although both should be fairly close. Neither will likely be able to do real-time encoding of 4K video though, so you'll need a GPU if you want to use hardware acceleration.

I use Ubuntu Server LTS for my Jellyfin server. Haven't had any issues with it, and it's well-supported and easy to manage.

Any stable linux distro should be fine, as you have experience with Ubuntu I would go with that. There should be plenty of support out there if you run into any issues too.

I use Debian because it was the easiest to get Docker GPU pass through working on.

My best decision was Unraid. I highly recommend

Openmediavault and then put Plex/jelly in a docker container.

Even though it takes a bit of learning, I would recommend just using a server Linux distro with docker. It does require a bit of learning, but it is well worth it. I would personally go with AlmaLinux, but Debian, RockyLinux, CentOS Stream, Ubuntu Server are also fine choices.

You can find docker images on dockerhub for pretty much everything, and even if you don't, creating dockerfiles isn't that hard. This is very convenient because you know where the configuration and data for everything is, you can easily control access (file system, ports, permissions), it's easy to update. And if you need to reinstall the OS, migrating docker containers is as easy as just copying the data and config files.

As everyone seems to comment what they run without advisory:
Debian + OMV6 and jellyfin (+reverse proxy) in docker.

DO NOT QUOTE ME ON THIS, but I might be mistaken, but having the drive be internal would help with random operations because the protocol is AHCI directly, but if it’s a hard drive, and given the use case, idk if it really matters. Using anything Ubuntu based probably supports hardware acceleration if what you said is true, so I’m guessing Zorin OS would be fine if you’re familiar with it (tho I personally don’t have the best experience with it)

I recently moved a lot of my services off my daily driver onto what will become a NAS.

I settled on Void because it has such good support for ZFS. If you're going to use ZFS, I would recommend Void.

Arch can be a bit unstable but it's simple to work with so that's an option.

If you run things in docker containers it shouldn't matter anyway, so ultimately pick something you're likely to use outside your media box, that way you'll be able to maintain it better.

As for remote access, I have a separate machine running alpine with wireguard in a docker container, I VPN into that machine to get access to other devices in the network.

I would very highly recommend using multiple smaller server grade HDDs instead of one big HDD, and software raid them. If on windows 10, use storage spaces. If on Linux, use zfs. Hard drives will fail and it's a pain in the ass to rebuild a 5-6tb media library when it does. Ask me how I know 😂

Also, definitely use internal drives. You can shuck the HDD out of the external enclosure and it will work perfectly fine as an internal drive. Bonus, you now have an HDD to USB adapter 😁

I'm personally using Windows 10 pro on an old lga775 supermicro server, with my old graphics card for hardware transcoding. Yeah it's inefficient and loud but that server board is stable as fuck and cheap as dirt. In windows 10 pro you can set group policies to basically debloat the OS, and there's also a great debloat script on GitHub. My idle CPU usage went from 20% to 3% just from the scripts and group policies.

I bought a synology NAS installed it on that, got some docker containers running sonarr/ sabnzbd etc.

DietPi (based on Debian). Incredibly lightweight. Easy menu system for installing apps easily which it then maintains and updates for you, or you can easily install Docker if you prefer that (or both). Contains a backup system if you want to use that too.