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When you are looking for a credit card for travel, you have two options - an airline co-branded credit card or a general miles rewards credit card. As you do not have particular airline to fly with, we would recommend you to consider travel credit card with miles. There are credit cards with big sign up bonuses that are enough for a round trip economy ticket. These cards usually come with an annual fee, but regular miles rewards rate is one of the highest. And there are cards with smaller sign up bonuses and regular miles rewards. These cards often come without an annual fee.
For example, the Discover it® Miles credit card may be a good option for you. This card allows to earn unlimited 1.5x miles on all purchases. What is more, Discover will match all the miles you've earned at the end of your first year (if you're a new cardmember). For example, if you earn 35,000 miles, you get 70,000 miles. Earned miles never expire and you can redeem them towards travel purchases - any airline ticket, hotel stay, cruise, car rental and more. The Miles card does not have an annual fee and a foreign transaction fee.
Bearing all this in mind, you can choose a travel rewards credit card with a sign up bonus that is best for you.