There was not a standard font on typewriters---there was a usual font that is found most commonly and that is a serif design. It was sort of the default design. Even among the serif designs there was much variation, as you can see if you carefully look over the hundreds of samples at http://typewriterdatabase.com/. Check especially the numerals and G g Q a e & and ? for a quick sampling.

Most of those typeface designs had distinctive names, although they are hard to discover now--check other resources at the URL below. Other fonts were ordered from among the different design options offered by the manufacturer. A large dealer might have stocked some typewriters with script and sans serif designs but mostly customers were happy with the usual.You usually only got to choose between elite and pica and NOTE that these are not typefaces but pitches, 12 characters per inch and 10 cpi, respectively.

Nowdays when we no longer have any choice at all, we have keep searching or take what we can find. As for what turns up most often in unusual fonts, I think you'll find different proportions in different areas.

Script designs especially differed a lot among various manufacturers. Today, people find--in order--serif (by far the most common), sans serif (aka gothic), script (incorrectly called cursive), squared (aka robotic, computer), and italic. These are on typebar machines; interchangeable single-element (golfball) and daisywheel machines are a whole different situation, of course.

And of course it is pot luck now for very understandable reasons. The Typewriter Database has on the front page a list of the 100 Most Popular Typewriters--but I suggest they are not the most popular, simply the most available, because we get what we can find, not necessarily what we want.