I'm just about to book an economy class oneworld explorer, with the following itinerary:

LHR-MEX-(surface)-TGU-MIA-BOG-LIM-(surface)-SCL-IPC-SCL-AKL-MEL-PER-AYQ-SYD-CGK-(surface)-BKK-LHR

Flights are split between BA, AA, QF & LA.

Which frequent flyer programme would it be best to join? I'm a UK resident if that makes any difference.

Thanks in advance for any help you can give me.