Serif fonts includes tried-and-true fonts like Times New Roman and Garamond. They are generally considered to be more authoritative and certainly more traditional.
Slab Serifs are actually pretty trendy right now. They include fonts like Courier and Courier New. These are bold fonts that always come across as “funky.” That’s seriously the best word to describe them.
Oh, the classics! Helvectica, Verdana, Arial, Century Gothic, and Calibri are all the classic Sans Serif fonts. I once had a design professor who said, “If you’re not using Helvetica, you’d better have a damn good reason.” I think that sums it up.
Perhaps the friendliest of the font faces, script (sometimes call handwriting) fonts are generally considered ‘creative’ or intriguing. That is, if they’re used correctly. Lobster can be a wonderful font, but used incorrectly, it might as well be Comic Sans.
This is sort of a made-up typeface. Let’s just all agree to call it ‘modern’ even if it’s usually charactorized as trendy-retro or european. Fonts that fall into this category include stuff like Eurostyle, Railway, and Lato (my favorite).
A quick look at Google Fonts and you’ll find the most popular fonts have been the same for some time (in order of popularity): Open Sans, Roboto, Oswald, Lato, Droid Sans. And ALL are sans serif fonts.