Should I be getting a private or public hospitalisation plan?

The best is to get private insurance (especially if you are young), as your early years are the most profitable years (in terms of income, skills and brain development). As you age, going to 50s / 60s, you can opt for Public Hospital A Class (which is decent and you may not need very expensive / immediate treatments).

And when you reach retirement age, affordability becomes the most important factor (as you wouldn't want to use your retirement funds and over insure). Downgrading is easy, upgrading is hard.

Your age matters too, so do let us know more details to give better advice.

Private if you can afford it. Public if you can't.

In the event of a concios decision, sure you can choose to go to a public hospital if required.

But in the event of an emergency or an unconcious decision, you'll be taken to the nearest hospital, and if that hospital just so happens to be a private hospital, you'll be glad you have full coverage.