It's all random.
You'll either be put on the German or Allied side, and thus you only have available the planes for each side. Sometimes you upgrade your favorite plane (let's say it's a German plane) and then the next mission (or few missions) you're put on the Allied side. Grrrr don't get to play with your new plane, but that's how it goes.
As to the games, they are random too, you can't choose to do a dogfight mission, unless you quit and join another game, over and over until you finally get into a dogfight mission.