You can choose any doctor and a List of some of the best Hospitals in Mexico to choose from.
On the Focus site you can view a huge list of Hospitals by State in the U.S. and there is a list of Global Offices for Best Doctors. Since this is Worldwide Insurance, you can use anywhere you go.
Regarding being eligible, you do not actually need to even have a Residency Visa. You can join on a Tourist Visa – FMM (since Feb) providing you live in Mexico 6 months or more a year and have a Mexican address.
The Policy continues forever (or till you move on) providing the premium is paid. You can join the plan up to age 74 years 11 months, but once in are in for life.