I'm in Melbourne, and I am going to assume Sydney will be similar to Melbourne.
I don't know how well off your family is, but I used to spend about AU$800-a-month.
That was because I used to live by myself, and I didn't think it was worth cooking for one person.
This year I will be living with my brother, so its more worth it to cook for two people. I guess I will be saving money by not eating out all the time.
Accommodation can vary depending on your standards, but generally I'd say about AU$250/AU$300-a-week (excluding bills) for property if you plan to live in the city, and it will get cheaper if you plan to live further away from the city.
Once again, if you have a housemate, living weekly expenses for food, etc will be cheaper. I recommend you get a housemate, as you can split groceries, utility bills, etc.
Not so sure about Sydney's public transport system, the last I went there was like 10 years ago I think, so I can't really remember.
Take it into account this is based in Melbourne, but as I said, I expect Sydney to be quite similar.
And I am not sure what it's like in Perth at all, as like Sydney, I went to Perth also 10 years ago or so.
It's always cheaper to stay with more housemates. Last few years when I left Perth, the average weekly accommodation per room is about $150-180 per week... Seems to be cheaper than the eastern state... Food out there I heard per meal is about $10 per meal. Of course cheaper to cook yourself:)