Qantas only charges a one off fee for joining their Frequent Flyer program, and if you're joining from the UK then there's no fee as far as I'm aware. They dropped the annual charges a couple of years ago.

As for joining BA, my understanding is that the program isn't as generous unless you buy your tickets up the front of the plane. Plus they've killed off their program for memebers in the South West Pacific and advised them to join up to Qantas FF program anyway, so seems like it would be a better choice if you'll be moving out this way.