Push notifications vs basic notifications/alerts

In our Reading app, we already provide basic notifications (or alerts) - e.g. if someone has followed you, someone liked your article, you've gotten 20 likes, etc.

We would like to test out push notifications. For example, "John Smith recently published US Politics". What would be the best use cases for push notifications without it being overkill? Examples for push notifications:

  1. Popular article posted by someone you follow (but if you follow multiple people, how do you decide which one should be featured as a push notif? Perhaps this person has to be more influential vs other people you follow? Or this article has more likes than others?

  2. If your followers recommend an article - e.g. "John, Sharon, and Mike recommended US Politics"

  3. Trending now: US Politics

Basically, how do you best go about push notifications without ruining UX?

Which push notifications should be sent out without overdoing it?