Australia to Beijing.
If booking the seat for your grandmother then make sure you get an aisle seat.
As LHR/MEL/Europe suggests a Chinese airline maybe preferable if your grandmother does not have a good command of English.
The other essential thing is to book a direct flight, as changing planes adds more complications and time to the journey. Some of the Chinese airlines you mention may not have direct flights. Air Asia don't have direct flights.
The Qantas A330's that will be flying to Beijing are certainly not old and horrendous, and Qantas are offering some good fares.