If your goal is rapid accrual, look for the card with the best bonus. Also consider which airlines fly the routes you want. For example, from the Dulles, United has lots of direct flights to Europe. You could sign up for the United credit card, which comes with a 30,000 mile bonus, or you could sign up for the Chase Sapphire preferred, which comes with a 40,000 point bonus (you can transfer the Chase points to United). I would go with Chase, not only for more points, but also because if using the miles doesn't work out for your trip to Europe, you will have more choices of how to use them. And frankly, redeeming miles for a summer flight to Europe is not the easiest thing to do, so you may be glad you have other options at your disposal.