How do I choose a matching font for my game?

I am currently in the midst of making an iOS game. So far, I created an overall look, i.e. figures and backgrounds. However, I also have to display textual information to the user. This makes me wonder which font to use. For this, I created two mockups with different fonts.

This one uses Avenir Next (which currently is one of my favorite fonts) with weights "Regular" and "Medium":

This one uses Action Man with weights "Regular" and "Bold":

Personally, I like both mockups but would prefer the second one with the Action Man font, because in my opinion, it fits better to the overall look of the game. However, Avenir Next is probably better readable, since the font size is rather small. But I also think it kind of breaks the design, although this might not be bad.

Therefore, my question would be: is it ok to use a rather round font when the surrounding design is also round or might it be better to use a font that breaks this paradigm.