I am fine with HD displays, but I would like to know where I can find how to design for LED driven displays where the LEDs are 6mm apart or 22mm apart. What resolution would I be looking for?
There's no standard resolution for such displays. They're generally made up of a collection of individual (usually square) panels or "tiles", of say 16 x 16 LED pixels. You can construct a display having hundreds of tiles horizontally but only a few tiles vertically, like the Fremont Street experience in Las Vegas, which has an aspect ratio of about 14:1 (2596 x 184).
Plus, displays can have any shape, not just simple rectangles. Fremont Street is curved, and I've worked with diamonds, cylinders, triangles, skewed pyramids and truncated circles.
There's no perfect way (that I've seen) of simulating the pixel grid. The best you can do is work in the pixel dimensions supplied by the display company, applying masks as needed for irregular shapes, and field test with any material that needs fine lines or small text. Assume for the most part that the intended viewing distance will allow the coarseness to 'average away'.
If you're using After Effects, when you create your comp, the only settings you need to define are the number of pixels horizontally and vertically, the frame rate, and the pixel aspect ratio.
If you know the specifications of your LED screen, (I'm assuming it's a jumbo outdoor screen), you should be able to calculate the aspect ratio from the physical size of the screen versus the number of pixels in the x and y directions.
e.g. if the pixels are 300x300 and the physical size was 3m x 3m, then the pixel aspect is 1:1 (square).
The fact that the pixels are a specific distance apart is less important than the ratios. When viewed from a sufficient distance, the gaps between the pixels shouldn't be visible.
If you wanted to get really precise about it, you could use a plugin like Trapcode Form or the TV pixel script to better simulate any aliasing due to lower resolutions (if it is a low resolution screen).
Most importantly, make sure you get "technical delivery specifications" from whoever is signing-off your final output. That way you shouldn't have any surprises at the last minute.
If you are a first time investor in outdoor LED signs, it is better to do plenty of research and find a trusted LED sign manufacturer who will not want to just make a sale but genuinely help you out as a customer.