I'm looking to purchase an (USB) adapter for WiDi/Miracast use. How can I (before purchase) determine if a WiFi adapter supports wireless display/Miracast?
WIDI support related to graphical card support, not wifi adapter Miracast has also nothing to do with CPU, it's a feature in modern wireless WiFi Direct network adapters (list of WLAN adapters supporting Miracast). Additionally, the display adapter must support Windows Display Driver Model (WDDM) (almost all modern display drivers support it).
If you want to send out your screen image over WIDI, you don't want a WIFI dongle, instead there are WIDI dongles which attach to your HDMI output and get power over a USB cord. Have a look at the Microsoft Wireless Display adapter for an example. At the least you're looking at around $30 for a generic Miracast dongle, but a WIFI dongle alone won't get the video signal to transmit it to a remote display.
Certain laptop motherboards (usually ones which are built with a mostly-Intel chipset) have internal WIDI since they can route the video from the internal video to the WIDI chips, but these are kind of rare.
Hope this helps!