For granular control over what notification emails get sent to which staff you can see the list here. There are a few things that can be controlled such as your general customer service email and if 'coaches' get notified of a new lead or not, but for the most part we air on the side of caution and send more to all rather than less.
If you feel like your inbox is getting junked up with too many email notifications from PushPress, its best to use the complex filtering that comes with whatever mail client you use (gmail, inbox, mac mail, outlook, yahoo etc). On that end you can set up rules to auto archive emails you don't want.
A big project of 2017 will be overhauling the communications on the PushPress side so you will in future have more control of this on the PushPress side, rather than your email client.