I am looking at the Roku3 -- good choice?
I like the Chromecast (which in this instance is for all intents and purposes the same as the Amazon Fire Stick, I've seen both) and Roku as the best two clients... as mentioned, the Roku 3 is more expensive but adds the advantage of being Indigo-controllable unlike the Chromecast/Fire Stick.
Is the mac mini going to be underpowered too? Time to upgrade?
Most likely not, but as mentioned if you have a bunch of concurrent transcoding sessions then you could see some slowdowns. If you store your movies in MP4 format, you may not even see much transcoding (though audio codecs come into play a bunch on certain devices, but audio is MUCH less intensive than video to manipulate.) I would start with Plex on the existing Mini and can always transfer to another should you find the need.
So, if I understand things, I should be able to store my video on the DS214+, run Plex on the mac mini, which will index the DS214+, and then stream to the Roku, which will provide the user interface on the TV and iOS devices, and overall control. Correct?
Yes, that should work fine -- on iOS devices the Plex app is pretty good and can play directly. In terms of your other content, I would personally not recommend having Plex attempt to read them via a network share; I tried this and it wasn't all that good (shares go to sleep, computers power down, etc.) So I would move that other content to the NAS if possible.
Adam