In the Forgotten Hero story, you are given choices at the end of some matches that will determine what card you get as a reward. The card you do not get can be soul summoned or earned from a pack later.
The rewards are set up differently for the non-tutorial stories. Each story is associated with a set of cards, and the only way to earn those cards is finishing the story missions. As such, the choices you can make don't affect what cards you earn, but which cutscenes you see and titles you earn.
If you bought the Isle of Madness Premium Pre-Order, all normal rewards will be replaced with Soul Gems and Gold equal to the amount of Soul Gems received from Master mode.