From a parent who's had a few different experiences.
Provide a comment box for parents to provide anonymous feedback if they wish, I tend to openly raise things but I have known others when they have issues to want to have a way to raise without their name
Provide updates when there are staff changes including temporary staff changes which provides the names of the staff in charge of the children and their qualifications
Involve parents in meeting new staff as well as yourself as a new manager and have review meetings with the parents to check the child's progress as well as any feedback they have on staff, menu, daily updates etc
Provide the rolling menu updates as soon as they come out and communicate if there will be deviations to this, some parents use these menu plans to plan their own meals (e.g knowing child will eat less of X meal and they do a full dinner that night, more of another so they do a light tea that day etc)
The ideal nursery would provide a middle of the day update for parents just to say all is fine, or live updates rather than just one at the end of the day, especially when child has just joined