You will, probably, have a terrible experience if you try to use the little 16gb Shield as a server. It, probably, will kind of work but you will be VERY limited as to what you can do.
Plex cannot use any form of attached storage for its database so there in a good chance you will run out of storage trying to use the 16gb Shield as a server unless you have a VERY small library or you turn off virtually every feature that uses any storage.
On the other hand (you have different fingers) the 500gb Shield Pro makes a wonderful server. During initial setup the Shield sometimes slows down and does not work well but once it finishes getting metadata and other info it speeds right up and works even better than the PC server I have with a processor that has a Passmark of over 8000. On top of that the Shield uses hardware transcoding and that allows even better performance.
So my vote for a Shield for a server is 16gb NO and 500gb YES.