What a efficient mobile phone (voice & data) options for a multi country trip

Plans that include T-Mobile's Simple Global are the best deal for having a single plan and number you're reachable at, if you have US residency or are an American citizen. The cheapest eligible plan is $50/month if you provide your own unlocked phone. T-Mobile's contracts don't have long terms like many others do, you can cancel your plan as soon as you return from your trip if you don't have a use for it. Free text and free 3G data roaming is included and calling is $0.20/minute in 140 countries (all of your destinations except for Fiji).

Alternatively, you could buy a local pre-paid SIM card in each country you visit. SIM cards with basic data are very cheap in many countries $5-15, the amount of data and time it's active varies and is very limited for instance in Australia.

In terms of "emergency", I would be surprised if your network provider doesn't have arrangements with the local providers in the countries you mention, even if you have to pay exorbitant rates. Except for mainland China, I don't think I've visited any county with zero connectivity for me.

Infrequent texting in my experience is not expensive, certainly less than a US dollar per text sent, and free to receive.

Data charges are another matter.

The U.K. network "3" has a pretty good system called "Feel at home", where roaming fees are not applied in many countries, including several of those you mention. But I am unsure if it can be easily set up while outside of the UK.

If like me you need to be reachable on your usual number then local SIMs are not an option. But if you don't, then buying one at the airport and disposing of it as you leave is probably the easiest route to go down. Of course some countries impose restrictions on how readily SIMs are made available, so it's worth checking in advance.