Planner needs to better inform users of new activity, and any email notification system (see my note below that it is not working for us) is going to bombard users with too many emails. The user ought to be able to view new activity with at least the follow: (a) new plans of which I am a member; (b) new todos that are assigned to me; (c) todos previously assigned to me that have new activities; (d) todos that are due today; (e) todos where the work is scheduled to begin today; (f) todos that are past due. Right now, my assistant has to tediously review her todos at the beginning of the day and try to figure out what is new (again, we are not getting email notification, and the users comments on them on this site have not been very positive).
By the way, the email notifications on new activity are not being sent out to our users. This feature does not appear to be working: https://support.office.com/en-us/article/Get-email-about-your-tasks-and-plans-cce223d6-b0ae-43cf-a080-266e2414a859 When we create a plan we get email notifications about the new "group" (those emails are useless to us), but we are not getting any emails about plan activity.