Yes Plex would be a good choice for this, another similar app which I prefer is KodiTV.
Plex on an iPad/iPhone can work in one of two ways and might need different versions depending on your choices. One way is for a Plex app to play content stored on your Mac on the iPad screen, this does not sound like what you want, the other way is to make the iPad/iPhone in to a remote control for the Plex application on the Mac.
This is the first approach - https://plex.tv/ios
This is an example of the remote control approach - https://itunes.apple.com/gb/app/plex-co-pilot-media-remote/id817719884?mt=8
There is another remote control approach. This involves using a 'smart' remote controller like a Logitech Harmony Ultimate remote. You would be viewing Plex running on the Mac on your TV and would use the Harmony remote to 'control' Plex running on the Mac, by pressing buttons on the remote you can navigate Plex menus, press play, pause, etc. It is even possible to do this approach using the old Apple infra-red remote http://www.apple.com/uk/shop/product/MC377Z/A/apple-remote or an Apple Bluetooth keyboard.
The Mac mini has analogue audio built-in in the form of a 3.5mm mini-jack connector. You can connect this to a matching socket on an AV receiver or use a mini-jack to RCA cable. You can configure the Mac to send audio via this connection even if it is using HDMI for the video connection. Some TVs offer the ability to receive audio via HDMI and send it straight out to another device also via a 3.5mm mini-jack.
Yes there are USB to RCA DACs for the Mac but I see no need to splash out on one.
Note: Both a 3.5mm mini-jack and an RCA connection are analogue only connections and only support a maximum of stereo 2.1 sound, i.e. left, right, and sub-woofer. For 5.1 surround-sound you need to use a digital connection i.e. a TOS-Link optical connection which the Mac mini also has built-in or send the sound via the HDMI to an AV Receiver.