Bad answers.
You did not supply enough information. What type of content will your server be serving up, and what type of clients will you be sending the content *TO*? Also, how many clients might you want to send content to simultaneously? These are the critical questions.
Example 1) If your source content is already in an iOS-friendly format (MPEG4), at a bitrate similar to what Apple sells as HD content on the iTunes store (perhaps you converted HD movies yourself using Handbrake), and your clients are things like a recent model iPad or iPhone, the base model Mac Mini is plenty capable enough, because Plex Media Server won't need to do any real work. It won't need to transcode the content, it just needs to push it across the network as-is, like a file server. In that scenario, you could even get by with a Mac Mini from 6+ years ago as your Plex Media Server.
Example 2) If your source content is high-bitrate MPEG2 (e.g., HD television broadcasts), the iPhone/iPad/AppleTV doesn't support that format natively. So, now Plex Media Server has to do on-the-fly transcoding to convert it to MPEG4, but retain it as a high-bitrate (e.g., 10Mbps+) 1080p format. That will require a good amount of CPU power. If you're only serving the content up to a single iPad in your house, the new base Mac Mini should still be capable of doing it.
Example 3) Similar to the #2 above, but you want to send videos to 3 simultaneous people in the house. The new base model Mac Mini may not cut it.
Note that I haven't done actual testing of the above scenarios with the new base model Mac Mini, but the principles expressed should be correct. See
this page on the Plex website for more info.