We would definitely be using paid Y tickets. Given the fact that the flights are so long, the most important thing we're looking for is upgrades. Lounge access would be nice too. And when we use the miles to redeem flights we'll be redeeming C (maybe F) tickets.
The problem with selecting the airline that I fly most is there's not really an airline I fly most. In the past I've flown DL, SQ, MH, and CX. I've never flown the same airline twice, and I would have very little control over which airline we would fly with.