Firstly, do you have private health insurance with Obstetric cover? If not then forget about going private. If you do it's another thing to consider.

Certainly many (probably most?) people go public, usually under midwife care. If you have a normal healthy pg you will just see the midwives for each visit. If they think you need to be checked by an OB they will organise that. Otherwise you will be cared for during your pg and labour and delivery by midwives. Whether or not you see the same midwife each time I think depends on what sort of program your hospital has.

There is also shared care which is as Sarah described above.

Hopefully Kelly or Alan or someone will come in and explain more to you about midwife care, I'm not exactly qualified!

Good luck with your decision