Assuming this forever-young-vaccine could be not expensive and accessible to anyone, in such a society sooner or later we would know each other very well as most of the people would always be the same people.
Natality control would be important.
How would power be managed in such a society? Security would become super-important as rich will be more secure and would be almost eternal.
I think there would be a big war before getting into a stable society with stronger separation into classes as they would have to separate physically to avoid intrusions because in this society it won't be only about money but about getting eternal.
What movie has described this scenario already?...