Well my 2cents would be for United - though guv1976 makes a good case for AA. Here's my logic: For your Turkey, China and Japan trips there are direct flights with Turkish Airlines, Air China and ANA. Greece requires a stopover but there are multiple routing options on Star Alliance partners. Your South American destinations are covered direct by United it self. Someone else with more international flight experience up front could chime in on the First/Business class quality comparison between these partner airlines but I normally go coach to maximize my distance anyway. Whoever you decide to go with - I'd add their branded credit card to your wallet for both the signup bonus and also the flight perks - United has first bag free, priority boarding, double miles on ticket purchases, etc. and the others are similar I'm sure.