I am a partner in a travel agency that is in Australia, the US, and does lots of tours in China. We need to have the ability to receive payments from customers anywhere in the world, and then have those payments deposited into either our US or Australian accounts (probably via PayPal), and soon into a China-based account. Further, we need flexibility about where we withdrawal: either in the US, Australia, or China; and the ability to wire money back and forth from any of these locations. And of course part of our goal is to avoid currency exchange charges as much as possible. Because we have no experience with this, any help is appreciated. Would definitely consider a call if you have specific and cogent expertise here. Thanks very much.
I believe that you may be over-complicating this a little. Typically, you need to have either citizenship or some other legal presence within a country to open a checking account within it. I would recommend establishing accounts in your own country first and then using ATMs in other countries to withdraw money, as "wiring" money internationally can be expensive. If you just need to pay for expenses while abroad, look instead into using credit cards that have no foreign transactions fees such as the Capital One Venture Card. If you really need accounts in multiple countries, you will likely need to incorporate within them.
As for accepting payments in different currencies. Your best bet will probably be 2Checkout or Stripe Atlas to start. Stripe Atlas will probably have lower fees but will take more technical expertise to get up and running. Best of luck to you!