Use two fonts in your design
Using too many fonts will hurt your website design. It adds unneeded complexity. So keep it simple and use two fonts. A serif and sans serif will work, but two serifs (or two sans serifs) can also work if they look different enough from one another.
Don’t use three or more fonts unless you have a good reason. A few years ago, I designed a site for a tech company that needed to show code snippets throughout their site. Neither of the two fonts I was using looked good in code. So I introduced a third font just for the snippets. In this instance, making the code easy to read was more important than the gestalt of the entire site.
That was an exception to the rule that made sense. But usually, two fonts is best.
What fonts should you use? Check out Typewolf. Not only do they feature great fonts, they also have suggested font pairings for each one.