I have been very privileged to have had access to both good public and private medical care through my entire life and then I moved to Brazil...
A quick summary, if you haven't followed this blog from the start: We chose to move here after my husbands move to Brazil was cancelled in the 2008 crisis. We decided to move here on our own, after our first daughter was born in the UK (National Health Service, fabulous, thank you). We travelled for 4 months before arriving in Sao Paulo, and when we arrived we processed our visa ourselves (my husband joined a Brazilian company as a co-founder so our visa was not a normal sponsored expat one, with included health care. As we were travelling for months before, and we arrived in Sao Paulo on tourist visas, we made sure we were covered on travel insurance.
The problem was when our visa (finally) was approved in September 2010 we weren't covered by travel insurance in Brazil anymore, since we were now residents. We didn't work this out until February 2011 when I had a slight panic as I realised we hadn't been covered for months at this stage. This is a country where a doctor's appointment cost R300-400, and then there's medication on top of that (go "generico" rather than branded). Some drugstores have loyalty cards and for some medication you can get discounts (you will need a CPF number to register for a loyalty card).
We used a great health insurance broker called Pacific Prime who I highly recommend, and we selected the best options for our family being based in Brazil. This was essential for us as I fell pregnant that same year and gave birth to our second daughter at Hospital Sao Luiz in November that year. In 2012 my husband was able to move company to another local company* and with this contract we gained local health care insurance with a company called OMINT.
When you choose your doctor, dentist, clinic, hospital it would be really helpful if they accept your local health insurance directly otherwise you will have to pay yourself first, and claim it back from your health insurance. I thought Fleury Clinic took my insurance but they don't, and I paid for my tests upfront (more than R$3000 worth of tests!). Also, always check with your doctor whether anything they prescribe you is really, really necessary. If you are paying for your own medical costs they can advise re: cheaper clinics, only doing necessary tests and if you have the "jeito" you can buy your medicine overseas.
I am of the belief that you do not need to go to the doctor for every scratch, sniff and cough. Drives my Brazilian friends crazy but even with health insurance covering our doctor visits, I don't believe in unnecessary and expensive... it should be for the necessary and free.
*He was able to move company as we started our application for permanent residency, based on our second daughter being born in Brazil. You do not have to wait for your PR to be approved to move company. We are 1 year into our application and we have our RNE Protocolo (piece of paper with our photo on + details + an official stamp) as we wait for our actual plastic cards to be processed and ready for pick up.