Well, only tested with Chrome and Firefox.
Somewhat arbitrarily choose Roboto and Roboto Mono because Roboto is a san-serif font that we were already using and because it has a monospaced version that matches (more or less).
Also set the line spacing to 1.5 so it's not too cramped for mobile and desktop.
Let everything inherit the font-family from html instead of specifying a font-family for each header type. (We were using the same set before anyway.)