Best Star Alliance programme to join for travels around Oceania/Asia?

I’m a member of Qantas Frequent Flyer but am travelling from Frankfurt to New York via Oslo on Scandinavian Airlines. I’m looking to join a Star Alliance programme to benefit from these airmiles but most of my travel will be Oceania/Asia in the future. Any suggestions/recommendations would be greatly appreciated as I feel like my head is going around in circles trying to figure this all out!
Thanks so much in advance!

Krisflyer works well for Aussies. Have a look. (Singapore Airlines)