Hey everyone!
So I finally did spend an afternoon searching through my web design stuff to find suitable fonts - and I did.
Overall, I settled with three fonts: Della Respira, EB Garamond and Myriad Pro.
I don't know if I need to, but here are some explanations why these and where they should be used.
Della Respira is the headline font. Originally, I intended to select an ornamental or at least decorative font, but later decided against it to keep the font more versatile and readable. Della Respira is an elegant font with very small serifs and a small Unicode character set (which is intentional for headlines).
The serif font
EB Garamond should be used for content. It is the free version of the propably most copied humanist typeface ever (since 1592) and has a relatively large character set (compared to other free fonts).
My last choice,
Myriad Pro, is also very common (especially in web design), but differs from the other two in that it is a sans-serif font intended for purely navigational purpose here. In other words, don't use it unless there is no game content (e.g. the filter options for characters or the top bar). Use the semibold version for headlines and the regular version otherwise.
Have fun!