Congratulations on your new startup.
Many of the countries you mentioned have complicated requirements for registering a company. You may need high capital or a local venture partner. If you solve this in each country you won't have time to focus on your business any more.
If your tax situation with Australia permits it, Hong Kong is a good general-purpose company location for Asia. The cost is at the lower end and you have access to the best banking infrastructure in Asia. Singapore is another good destination, especially if you are looking to use it as a holding company for all your local entities.
Concerning payments, I'd start out using CurrencyFair or Transferwise to channel payments into "virtual" local bank accounts. If your transaction amounts are high enough, you can also do international T/Ts. Those will cost you about 25 to 30 USD/transfer.
There are also some countries that have adopted Chinese payment gateways, like WeChat or Alipay. Maybe this can work for you as well.
Be sure to let us know for what you decide and how it goes.