it was an odd journey to find out that sanserif was for the computer screen, serifs for the printed page.
Well, except that sans-serif typefaces have been around longer than computer or TV screens, like 200 years before. Which is not to deny that at one point, sans-serif typefaces worked better on monitors. There's one typeface I know of,
Lucida Fax, that was tweaked for use with fax machines.
Generally, serif for body text, and sans-serif for large text like headlines and signs.
Another major division in typefaces is whether the letters have combinations of thick and thin strokes (eg. Times, Optima), or just a single thickness used for all of the letter parts (eg. Arial, Courier). The smaller the text, the more you need the thick/thin combos.
i haven't looked into it but there's probably some theory about this.
I gather that typography is a really complex craft. Much of it deals with subtle differences that are intended not to be obvious. If you
notice a typeface, then it's harder to read. It's probably changed a lot over the years, with things like computer-specific typefaces not having to deal with
dot gain, but they do need to worry about dithering.