Smallest hi-res HDMI/Thunderbolt display device for Mac Mini

The short version is that I essentially need to have an HDMI or Thunderbolt display attached to my Mac Mini in order to select a higher resolution (1920x1080 or higher), however I don't want a monitor actually attached to it if I could avoid it being that I only use the Mac Mini as a remote device via Screen Sharing.

What is the smallest/cheapest way to accomplish this?