OSDE is just the name of a brand of private health insurance that is not attached to a specific hospital. (Like a Blue Cross in the US)It is widely considered one of the best because it has a very large roster of high quality participating doctors and uses the best private clinics and hospitals. They offer various plans at various price points. You just go to one of their offices and they will talk with you and show you their different plans (their largest office is at Billinghurst and Santa Fe.) OSDE and other similar plans such as Medicus also offer wide choices that don't restrict you to one hospital and it's affiliates
For the thrift minded many of the private hospital systems such as hospital Italiano, hospital Aleman, hospital suiza, and hospital Britannico also offer their own health insurance.plans, however you are restricted to only using providers directly affiliated with their institution Again they offer different plans at different price points I know people who use these plans and are happy with them
I have one of the cheapest comprehensive OSDE plans, but nevertheless there are no copays, limits or deductibles except for outpatient medications where I pay a deeply discounted price for prescribed medications. Generally speaking all these plans offer you much shorter wait times and nicer facilities than public facilities, altho many times the public doctors are equally as good. Just harder to access!