You won't be able to get all your visas in advance. I know China's visas are only good for 90 days and they seem unwilling to budge for US citizens even when there are other options officially listed. (There are longer-term multi-entry visas that we should have qualified for but my wife couldn't pry anything out of them despite spending over an hour talking to an official in Shanghai. We wanted to keep a current visa at all times because we didn't know when her mother was going to die.) I feel like Australia has the same limit but that was half a lifetime ago (and the rules might have changed even if my memory is right.)

I have been on two long many-country trips. We always got visas by applying for them in the country before the country we would need them in. The only time this was any sort of problem was with a visa for Indonesia obtained in Australia. The problem is we weren't sticking around in Sydney and they wanted something like an eternity to process it. We ended up having to have our passports mailed to Darwin for us to pick up from the post office.