Even though some NAS providers advertise their products as "having" Plex Media Server apps, all but the most expensive and powerful cannot actually perform video transcoding, all they can do is direct play and direct stream content. This is fine if all your devices support the media you have, but it is very restrictive and misleading.
Video transcoding is very CPU intensive task and consumer NAS boxes have low powered CPUs, they aren't designed for CPU intensive tasks.
You can store your media on a NAS and use a PC to run Plex Media Server to do all the heavy lifting, however when you factor in the cost of a NAS and the hard disks, to me it made more sense to either use an existing PC or a new custom built PC and add the hard disks directly to the PC. This also reduces the latency of accessing the content from the NAS over the network.
After deciding against using a NAS for Plex, I went about checking what the requirements are to run Plex Media Server on a PC.
My current PC is old and in need of replacement, but perhaps I could upgrade the storage and when I buy a new PC at a later date, the old one can become a dedicated media streaming box?
The Plex website has some guidance on how much CPU power you need for running Plex Server. Based on the benchmark score of 3057 PassMark for my old CPU I was able to confirm it is capable of streaming at least one 1080p stream.
The alternative would have been to build a new custom PC especially for Plex, but I don't have that sort of spare cash at the moment.