There are several considerations to make while choosing a font. The font needs to be readable for all users.
Does the content come in several languages? Make sure to check that all character sets for any foreign language are available. Users can also translate the content with a browser plugin. So you might not even know what languages your users use.
Make sure your selected font(s) contain all the characters required to set the text. There shouldn't be any errors, regardless of language or alphabet. All extra characters increase the size of the fonts to download and make your site slower to load. But they can also improve accessibility. So take this into account when you are selecting your fonts.
Thin or light fonts can be harder to read because they have a lower contrast against the background. Make sure your selected font(s) work well on both standard-resolution and high-resolution displays.
Use fonts that have clear letterforms and enough spacing between characters.
Sans-serif fonts like Arial, Helvetica and Open Sans are often recommended for online content. Whatever fonts you end up choosing, make sure to also provide a fallback font in case of problems with the chosen font. On the code side, people usually define a font-family to ensure the text can be readable for all users.