With gmail, you can assign labels or tabs to certain emails. Then use the label manager to determine notifications. You can find more information at https://support.google.com/mail/answer/1075549?hl=en, Go to that link, then expand the Android dropdown for detailed information.
Here's an excerpt...
Limit your notifications to messages you care about. For example, maybe you’d like to be notified about Updates but not Promotions, or only messages with the “Urgent” label you created.
In the Gmail app, touch the menu .
Choose an account.
Make sure that Notifications is checked.
Touch Manage labels.
Choose one of your labels.
Touch Sync messages and choose either Sync: Last 30 days or Sync: All.
Check Label notifications.
Choose how you want to be notified.
Repeat for any label you want notifications for. You can choose different ringtones for different labels.
Note: By default, notifications are on for Primary, so you may need to turn off its notifications.
I have gone trough that. However what i want is not to only get notification from specific emails, but not get notification from specific emails addresses, and get notifications for all other emails(so that i get notification from new senders as well).
I would like the no notification emails to also go to inbox, (but having a specific label) but not to get notification from those emails.