I am trying to choose the best alliance and FF program. (So far, I have been been focusing on AA and thus flying either AA or its partners, One World or otherwise. Even earned 400k+ miles in the program to date, but now reconsidering the whole issue again.)

My home airport is ORD/MDW. Travel interest primarily DEL or BOM; secondarily LON (any airport) and NRT. Interesting stops en route to these are welcome too, but not decisive in themselves.

My main goal in a FF program would also be to earn these international tickets, not domestics or domestic upgrades.

Clarifications: (1) Most travel is economy, except rare ones paid by someone else. (2) Lounge access in a hub airport connecting between ORD and DEL, between two 8-9 hour flights, would be a major attraction, on par with free award tickets. Lounge access in ORD, DEL, or nearby airports like DTW or NYC is less useful though always a positive factor. (3) I do fly around within India once there, so participation of a regional Indian carrier in the program would be a secondary attraction.

Question: Is One World better than Skyteam and Star Alliance for my purpose? If so, which airline's FF program would be best to join, and which ones best to actually fly?