The best plex server is simply going on Craigslist and search for Mac mini. the oldest mac mini can be had for 50 or 100 bucks and can handle plex easy. your network on the other hand I can't speak for cause plex when viewing remotely can tax the network pretty good
Actually when talking about plex and transcoding full HD streams, plex has given suggested cpu specs. So while saying any old mac mini can handle plex is technically correct, it depends on what you are using plex for. If you are placing 1080p blurays on your server and want the ability for simultaneous people to be able to stream outside your network, that old mac mini will not be able to handle the load. Plex suggest a passmark score of 2000 for each HD stream to transcode.