Early on in Monster Crew you aren’t going to have a lot of Bonus Cards to choose from.  However, later in the game you’ll have a lot of them because you’ll have grabbed a few and you get some just by progressing through the story and completing quests.  The strategy doesn’t just become which card you want to play, but getting to the Bonus Card that you want to play.  The three cards you have available at the elevator may not be what you need at that moment, and you’ll have to use a Shuffle to try and get the card you’re looking for.

Keep this in mind when you are thinking about buying another Bonus Card for your deck versus upgrading an existing card in your deck.  It might be a better option to upgrade some of your favorite Bonus Cards instead of growing your deck.  This is all part of the strategy of Bonus Cards and Monster Crew.