I had considered Thuraya but heard the further south you went, the more trouble locating a satellite. They sure sound attractive though, only using a satellite when out of mobile range and are a good size phone
Iridium still seems the best option and would be good if you are a Telstra mobile customer because I understand that you can use your post paid sim card from your mobile in the Iridium phone. You can also call using regular phone numbers without having to add or delete number/s, as well as call 000 and 1300 and 1800 numbers. Phones are expensive and mostly involve a plan on a contract period (Telstra told me the minimum was $39.00 per month for 2 years), otherwise calls are hideously expensive on a casual plan. I have read that a $10.00 casual plan is an option but after speaking to Telstra, there was a reason why I couldn't do it. Maybe you had to already own the phone?? Iridium uses 66 odd, low orbiting satellites.
Inmarsat is the least expensive phone and is the pre-paid option. Calls to an Inmarsat phone are at international rates so very $$ and can't ring 000 (yet) and most 1300 or 1800 numbers and therefore need to know the local emergency numbers which may not be convenient or possible. Must point the phone in the direction of the geostationary satellites which I think are over PNG? Need to add the international prefix?? before the phone number etc.
Now this was only my take on things. What is best probably depends on the needs of the individual. I am almost certainly going with Inmarsat.
Providing I can call someone, say in a breakdown, it is better than being up $hit creek without a paddle. If it is a serious medical emergency, your pretty much buggered anyway given how long it will take for someone to get there and you may be better off driving to get help.