I want to buy a Raspberry Pi 3, and attach it to an external hard drive (or 2) that contains most of my media. While this is obviously simple, I want to know if the RPi 3 supports Miracast/Wireless Display. I have a Sony Bravia KDL 55W800A Television, and it is very fussy when it comes to screen mirroring, so I want to know if there is something that may break the deal when trying to create a sort-of NAS...
The Pi's doesn't inherently support any wireless display standards. You need to install and configure software to do any kind of streaming. 'Normally' (lots of different use cases here), I would just use an HDMI cable and strap the Pi to the back of the TV.
There appears to be an inactive (last update 2014) project called Piracast which could achieve Miracast streaming, provided you followed the instructions very precisely (specific USB dongle required, 3.5mm audio only).
A second workaround would be using a Chromecast. The latest versions of Kodi and Yatse will allow you to cast footage from the HD connected to the Pi via Kodi, to Yatse on an Android phone, then on to the Chromecast attached to the TV. Bit of a long way round but (so far as I've tested it) reliable.