best for what? End of the year is the most expensive time as Aussies are all rushing to Bondi for Christmas. You can go via HK, Bangkok, Singapore and I think Dubai. No way of knowing at the moment which will be cheapest. In terms of time they'll all be much the same.
In terms of avoiding jetlag on arrival go westwards ie via Los Angeles. You can even get a few days in Fidji on your way... then come back through Asia and avoid the jetlag on getting home.
I went via kula lumpa and wasn't too bad going out but was a bit of a wreck when I got back. Malaysian airlines were fantastic though and I'd recommend them anytime :c)
I usually fly via Singapore with Singapore Airlines or via Dubai with Emirates. Both airlines are great in terms of service,competitive pricing and good flight times/lengths of stopovers. If possible try to schedule your flights so you fly through the night on each leg and just take some herbal sleeping pills to knock you out! If you can work in with your body clock like this it definitely helps with the jetlag.