Welcome @tidden - sorry to see you here but glad that you found us. The waiting is hard but try to distract yourself if you can. Once you have a plan to focus on, it should get easier. That initial time post-diagnosis is a vortex of terror. You can read my cancer diagnosis by clicking on my username.
As far as costs, going through the public system, I doubt that you will have any...possibly, carparking? I did have private insurance which I used for surgery and chemo but I know lots of people go public without a problem. By the way, 4 weeks is not a huge time to wait. I know some women have gone in for surgery within days of diagnosis but my surgeon doesn't wait around and I was diagnosed on 5/12 with surgery on 21/12 to get in before Christmas and that was probably as much because he knew that I was so anxious. In between, I had a number of tests and scans to get done before surgery.
Radiation is where the costs add up and private doesn't help you with that, anyway. People can be thousands out of pocket but as you will be going public, there should be no cost at all...for the same treatment. The only difference I've been able to ascertain between private and public rads is the supply of moisturiser and maybe your own gown (which you have to wash yourself, of course).
Then, as @kmakm has said, if the cancer receptor type is positive, you will probably have ongoing treatment with some sort of hormone therapy. This adds up over time as it could be for 5-10 years at around $40 per month. Do your sums and check if you're eligible for a health concession card as this will bring it down to $5.40 per month.
I have not had reconstruction (not sure if I'm going to) and you don't say what surgery you're going in for, but if you are considering it, check with your surgeon to find out what the waiting lists are like if you don't make the choice immediately. I believe that in some states (Qld for sure), the waiting lists are years long in the public system unless the reconstruction is part of the original surgery. Other members may shed more light on this.
If you're working, it may also be worth checking your Superannuation cover as you may have Trauma cover or Income Protection. Time away from work may be minimal but good to know that if you must take extended leave, whether you can access some money and the restrictions around it.
You will know more about what your treatment will be when you get the pathology report back after surgery. Don't be afraid to ask your medical team about costs at any time during the process and tell them if money is an issue for you.
And check in with the forum at any time with questions, rants (or head over to Night Howls if you just want to pass the time of night (or day)).