It's pretty easy: Just set your Document size to be 1920x1080. If the screen is actually 1920x1080 where the signage will appear (and there is no pixel doubling), then you'll just need to include assets that are larger than that dimension. Hype automatically sizes content based on the size in the document. If you will be also showing this content on a retina device at any point, I recommend including images twice the dimension of their display size. This will ensure that retina screens get sharp images.
For best practices, use Text or Icons (as opposed to rasterized graphics of text) whenever possible to get the highest quality output.
The performance of your animation / document will depend on what is driving it (what kind of CPU / Graphics card), so I recommend testing extensively to see how your animations perform. If you have any issues please get in touch!