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Credit card benefits like free checked bag or priority boarding are often given by airlines co-branded credit cards, for example, Delta or United credit cards. Airline credit cards may be a good choice for you if you often travel with them. Keep in mind, that this type of cards often comes with high annual fees. But if you are not a frequent traveler of a particular airline, it is better to choose a travel rewards credit card.
You can use a regular credit card to pay baggage fees, to earn rewards, and then erase those fees using the card's rewards. For example, it can be the Discover it® Miles credit card. It allows to earn 1.5 miles on all purchases. Discover will match all the miles you've earned at the end of your first year, automatically. For example, if you earn 35,000 miles, you get 70,000 miles. That's $700 towards travel! Miles never expire and never devaluate. You can use miles as statement credits towards travel purchases, or you can simply redeem them for cash and use for whatever you want. The card has no annual fee and no foreign transaction fee.