Ok, so by my understanding of how this works, I receive:
+4xp +2rep (life) for a win against a higher lvl player.
+1xp +1rep (life) for using a mono deck of my element.
6 cards from my opponents deck.
-1rep (air) for a win against an Air player.
Then the rewards for completing "The Journey Begins" would be received once I return to... I guess my capital city, and perform a "complete quest" action.
Hopefully I didn't miss anything.