Free or heavily discounted medical for civilians is slightly complicated but still better than the NHS. Theres a medicare-surcharge to cover it. Also if your dependants don’t earn enough annually you may get a reduced tax refund as some will be clawed back by ATO. Aus citizens are encouraged to take out private health cover on top. In doing so their levi is reduced.
Some tips:
I hear if you plan to have children in Australia, it pays dividend to have private cover.
I have also heard more than one tale of private health not delivering the right or agreed cover for dental. Often charging for it in peoples 1st years of policy, then stating it is not effective until 2nd or 3rd year when a claim is made. Read the fine print.
Getting cover for some risks can be hard, but lifebroker.com have good rates for larger policies. There is a lengthy phone call to go through. They also send you off for a free blood test, but its worth it. (I am not affliated with or rewarded by lifebroker)
I insure myself for $2 million for what other companies wanted for a few hundred thousand in cover.
Note: If your work is going to be low risk, maybe a comparison site search may be more beneficial.