We used to run two Mac Minis as media servers, one per TV; as per the previous poster, they were fantastic in their day... but that day has well and truly past (for most people and for most purposes, he hastily adds!).

A key advantage at the time was the (relative) ease of fitting into a HT system - built-in IR, so it could be easily controlled by a Harmony remote; they also ran Kodi (sorry XBMC at that time) pretty well. That said, there were hassles with the Mini not going into stand-by (so wasting lots of power), there could be tricky issues with the sound output, plus using a computer (even when just sorting stuff) via a TV is a dog...

Over time we found fewer and fewer reasons to use them, ultimately replacing them both with Amazon Fire TVs

I think unless there is a strong rationale as to why you need a computer connected to the TV (and that you can't connect a laptop for the times that you need this) then you'll probably find a dedicated media box a better option - - one box that provides access to a wide variety of sources, (comparatively) cheap, low power usage, decent and consistent interface, and none of the hassles of managing and using a full computer...  

Agree with the above comments, my 2009 Mac Mini is very close to EOL. It's basically just a file server now, not used for displaying content on the TV much at all anymore. The last uses for it were doing web-based video playback - Sky-Go for eg, but that has been replaced with the very good Kodi add-in. In saying that I did try to use it on the weekend for doing a photo slide-show out of Photos, but the old girl (the mac, not me) couldn't cope rendering the images.

I can see it is going to be shortly replaced by a NAS, and just using in-built TV apps, RPi's for Kodi, and Chromecasts for other stuff. I'm not all in on 4K yet so that isn't too much of requirement just yet.

I have a MacMini that is connected to my TV as a media server (Plex).

The SSD and maxed out RAM make it nice and easy to drive, plus it can be controlled by my Harmony remote and the Apple keyboard/mouse combo in a third party holder arrangement makes things nice and compact.

HOWEVER, I will replace it with a NAS at some point to serve my Plex files.

Then the MacMini will be retired for its original purpose - a high end music playback device...

I have used Audiovarna on it in the past - it did sound good, but ultimately I know it will still be a mid-term solution as I will no doubt end up moving towards a full time Roon based fix via a NAS.

Thank for all the useful comments on using MacMini as a media player I think I will be looking at 

b) Nvidia Shield
c) Vero 4K+ ( Is there a NZ supplier for Vero 4K+ ? )