You do not necessarily need to transfer to the program of the airline on which you intend to travel. Most major airlines belong to one of three international alliances, and you can redeem through any program for travel on flights operated by all airlines in the same alliance.

That said, the major USA-based airlines are partnered with different card issuers.

American with Citi and Barclays.
Delta with American Express.
Southwest with Chase.
United with Chase.

No card earns rewards transferable to all four.

American Express Membership Rewards can be transferred to Delta, to partners of American and United, and to many others. No sensible way to use for Southwest. See THIS thread.

Chase Ultimate Rewards can be transferred to Southwest and United, and to partners of American and Delta. See THIS thread.

Starwood Preferred Guest is a hotel program, but they have an attractive airline transfer feature. Their credit card is issued by American Express. Starpoints can be transferred to American, Delta, but not to Southwest and the transfer rate to United is not attractive.

All three programs transfer to Virgin Atlantic. Bear in mind that Virgin Atlantic miles can also be redeemed for flights operated by Delta.

Airline pricing varies by market. Don't assume that if AA was high priced in one market they are high-priced in another.