Minimalist web design should use fonts that screen friendly and web safe fonts. Web safe fonts are fonts that are common along all version of Windows, Mac, Linux, etc. I recommend you to use 2 or 3 different type of fonts, for the title, content, and navigation.

Font-family property is a prioritized list of font names. Here are the list of font-family. I use this to help me designing website.

Arial, Helvetica, sans-serif
‘Times New Roman’, Times, serif
‘Courier New’, Courier, monospace
Georgia, ‘Times New Roman’, Times, serif
Verdana, Arial, Helvetica, sans-serif
Geneva, Arial, Helvetica, sans-serif
‘Arial Black’, Gadget, sans-serif
‘Bookman Old Style’, serif
‘Comic Sans MS’, cursive
Courier, monospace
Garamond, serif
Impact, Charcoal, sans-serif
‘Lucida Console’, Monaco, monospace
‘Lucida Sans Unicode’, ‘Lucida Grande’, sans-serif
‘MS Sans Serif’, Geneva, sans-serif
‘MS Serif’, ‘New York’, sans-serif
‘Palatino Linotype’, ‘Book Antiqua’, Palatino, serif
Symbol, sans-serif
Tahoma, Geneva, sans-serif
‘Trebuchet MS’, Helvetica, sans-serif

I also add screenshots of how they look in different web browser:

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