Kotton,
Australian Unity is a well known health insurer and based in Melbourne. My parents have been members ever since I was a small child (so nearly 30 years) and I can't say my mum has ever said a bad word about them!
Having said that there are a lot of insurance choices, with all different sorts of inclusions, waiting periods etc. Try this website -
www.iselect.com.au. A lot of providers now offer "minimum" plans which give very low cover, just so you avoid the 1%
additional medicare levy. Note that this is on people who earn over A$50k p.a. You will have to pay a 1.5% medicare levy on top of normal tax no matter what.
Going with a bigger insurer is better IMHO. E.G. when I lived in Sydney I used HCF, which had a huge dental centre in the Sydney CBD - I got 2 free checkups a year, including xrays and a professional teeth clean, which I thought was pretty good considering how much these usually cost back home.