That's more oompf than my Synology NAS, and it runs Plex just fine.

If it's just a storage and no transcoding then it'll be fine

My plex Container has four Cores and 2 GB RAM. Works fine with just one Core transcoding 1080p24 HEVC.

(Ryzen 7 5700G)

If you own the hardware, sure, use it. It will suffice.

If you plan on buying this ancient hardware, do not do it!

There is some really anecdotal evidence from the other comments.

Check out Haswell capabilities https://en.m.wikipedia.org/wiki/Intel_Quick_Sync_Video

It decodes h.264 and that's about it. Yes, plex does not transcode for free but hardware is hardware. Spending money on obsolete, lacking hardware is not wise.

If you are buying, go for 6th gen, 8th gen or 11th gen. These are the sweetspots that are either cheap, widely available or very capable.

A small check at https://ark.intel.com/content/www/de/de/ark/products/77486/intel-core-i34150-processor-3m-cache-3-50-ghz.html shows me, that the cpu supports quicksync. It means you can use hardware transcoding (if you have a Plex pass). Maybe the quality is not a nice as a more modern cpu but it will do just fine with 1080p videos. Should be a very ok Plex server - if you already own the hardware. I would not be buy this ancient machine to become my next Plex server.

it should be fine, your limiting factor is going to be number of transcode streams. When a plex client connects to a plex server and tries to stream a video the client and server will talk and discuss what formats the client can accept and if the video is not in that format the plex server will transcode it on the fly to a format that the client can play. The more powerful the machine the more transcoding streams it can handle at once. But realistically do you need more than like 2 or 3 at most? probably not.

Ample. There's not much processing going on, it's mainly shunting files around the network. Look toward improving that side of things to improve connectivity and user experience. A wired network is generally faster and more reliable than wifi, if possible.

My current build is a small quad-core Xeon from the Haswell era and does just fine. I added a Quadro P400 for PLEX transcoding. If the rig also did storage, it would also be fine. You’d be good if you wanted to add a Quadro card to yours.

If you ever get a system that supports hardware transcoding, consider jellyfin instead of plex, transcoding has no $cost there

I’d rather get an N100 minipc in this case. Similar performance but able to do media transcode a lot better

I was using a old Atom Netbook with 2GB RAM as a Plex server. No transcoding, but it certainly did the job! The only limitation was it was all from an external USB2 drive, but even then it was still decent depending on the file. No 4k files, but it worked with 1080p.