What is the minimum amount/thickness of insulation I can get away with?
In each climate zone, the Building Code of Australia has determined a minimum amount of needed insulation expressed in R-value (the efficiency of a material at stopping heat flow through it.) This should be the minimum you use.
For the sake of your budget, remember that more insulation isn’t always better. While more insulation than recommended will indeed improve your home’s heat efficiency, the law of diminishing returns means that it’s not always worth the extra cost and other issues (such as draught proofing) in your home may need attention first.
For this reason, discuss your insulation requirements and budget with a trustworthy installer.