I have one of the least expensive setups for basic health insurance cover and I can choose my own doctor. The most expensive packages do not guarantee anything or any quality. The basic cover legally is the same for all health insurance providers.
To register with a doctor here, you do just that, select one and register. If you already have your health insurance card, take it with you.
If you do want to save money, first choose your health insurance package. Then see if you have to choose a doctor from a list provided.
Health insurance comparison here: https://en.comparis.ch/krankenkassen/default.aspx