The translation for Quest is "búsqueda" but it just does not work properly. In English we say "I'm on a quest for the holy grail" this is not quite the same as "I'm searching for the holy grail." So how do I get the seance of adventure implied in "quest" in Spanish. Can some one think of a better word.
Yes, "misión" is pretty common, here are some example websites in Spanish using it in a game context: