There are others probably better placed to answer your question, but it always helps to give as much info as may be relevant, such as whether you have status on any of the airlines; the flight number (if known) and I'm assuming that you have points with all 3 schemes and that's your question?
QF upgrades are allocated on a hierarchical system with the high status pax having priority and seats then allocated down the 'food chain' until availability is exhausted. As a result I would not count on an upgrade if you are down the status line. As a gold (now, sadly) I have not had an upgrade in a long time. Obviously other higher status pax want them on the flights I have been on.
If you are flying a lot (a definition of a lot might be useful) then BA might be the go to program depending on your fare class. You do need a non-Australian address to join BA Executive Club. SYD-SIN/CGK earns 35 tier points each way at least on Qantas. More for flexible economy. 300, 600 and 1500 tier points to progress up the levels. So Qantas Silver equivalent after 9 flights in discount economy. Qantas is 30 SC, each way for the same routes. 10 flights to get Silver and gold, but fewer flight for platinum. Less flights to keep all levels with Qantas.
AA is miles based and I'm not as familiar with those requirements. Hopefully someone else will chip in.
Edit: Agree that as bronze you have an extremely small chance of an upgrade. Not as small as my chance to quantum tunnel through a wall, but close.