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Take a look at the AA and UA redemption charts, and Google "ORD airport wiki" to see what international destinations have nonstop service on AA, UA, and their respective partners. Note that UA charges more miles for premium-cabin travel on partner metal than on UA metal; AA's premium-cabin rates are the same across carriers.

However, AA assesses hefty cash surcharges for long-haul award travel on BA, and more modest surcharges for award travel on IB. No surcharges on any other AA partner. UA does not assess cash surcharges for award travel on any partner.

While you certainly can get a credit card affiliated with your first choice of carriers, that might not be necessary or even optimal. An Amex premier Gold or Starwood card, or a Chase Sapphire Preferred card would earn points that could be converted to a number of different airlines (and some hotel programs). But if you opt to fly with AA, certain Citi/AA credit cards will earn you a 10% rebate on AAdvantage flight-award redemptions, and also make available reduced-rate redemptions to various North American award destinations on a rotating basis. The other benefits you would get from an airline-affiliated credit card will be duplicated by frequent-flyer elite status, which you would earn after a few months of your anticipated flying. (If you opt to go with AA, you can look into their Gold and Platinum "challenges," which would get you elite status more quickly.)