For known signs, look for the printing quality. Reproductions made from scans or photos of old signs will look muddy as compared to the real thing, especially if the original used a halftone to reproduce an image because scanners and printers commonly available to a ripoff artist don't do a great job of reproducing them. Here is a scan of a 1921 sign meant for insertion in an Exhibit machine with a halftone image on it:
Here is a reprint I made from the scan using a photo enhancing program and a laser printer to clean it up as best as I could. The image is lesser quality than the original because of how the printer and scanner reproduced the halftone image:
A printed vintage sign should have crisp graphics and lettering. A reprint made from the original won't. The blank areas of the sign should be clean and free of printing spots--a good telltale sign of a reprinted item is printing where there should be blank background.
Research known signage. Odds are that the item you are considering is not unknown. If it is something totally unique and involves a major HOFer, you want to be extra cautious.
As far as different sizes go, it depends. Signage was designed practically, not for novelty's sake. Use common sense. Why would a manufacturer spend the money to make a sign the size of a piece of paper? Anything small enough to be a hand-bill is likely to be printed on paper or newsprint so that it could be easily carried and easily handed to pedestrians.
Anything intended for display on a countertop will likely have a built-in easel so it can stand up, or at least will have the remnants from the easel on the back.
One thing that is very tough to fake is brittleness of the board or paper. Old cardboard signage will usually feel brittle as compared to modern cardboard.
If the item is real photo, as some are, look for silvering. Very hard to fake.