We've always flown with British Airways/Qantas and had no complaints. Used them because they offer the biggest range of stopovers.

Rosalyn

You have quite a few to choose from, a lot depends on whether you want a stop over. I have used Singapore Airlines, Air Malaysia and Quantas for Australia trips.
Emirates also fly to Perth as do Thai. Air Malaysia and Thai usually have good service and some of the best leg room in the air, but Thai really needs to upgrade their planes. Singapore always come out top or near the top in polls for the best airline. I haven't any problem with BA apart from their cramped seating, which gets a bit old on long flights, Quantas also has pretty cramped seating though their new planes may be better.