Unless there's a material ticket price difference, we are AA exclusive. Starwood AMEX is, by far, my first choice due to (i) the bonus on conversion to AA miles and (ii) the ability to move points back and forth among members of the same household.

After that, I use Citibank's AAdvantage MasterCard.

Only exception is foreign transactions, for which I use the Schwab 2% cashback card since it imposes no foreign currency fees. I understand those are no longer available, so Capital One may be another option for foreign currency transactions.