I think you need to come up with a rough itinerary and buy a true RTW ticket, rather than just "pay as you go." I'm not sure if you've priced this out, but a RTW ticket will come out to be significantly more cost effective than purchasing separate one-ways. If you're not sure where you'll want to go, you can always buy add-on trips from various (hopefully cheaper) spots.

I'm not sure what you've budgeted for this trip in terms of airfare, but you may be pleasantly surprised if you look up the RTW rates.

In terms of which alliance to choose, I personally find Oneworld and Star Alliance miles and elite status to be quite valuable. You'll also have some pretty good coverage intra-Asia on those alliances. My choice would probably want to go with AA or United, but you'll need to decide what your goals are (free domestic/international tickets, upgrades on paid domestic/international tickets) first.