I receive monthly between 3,000 and 4,000 Emails. If I would've stop my work whenever I get an email, I would not do anything at the end of the day.
A solution represents Filters that Gmail offers its users (and folders and categories), but if you get the various emails from senders who have nothing in common, not even the filters can not do miracles.
SaneBox promises to sort messages according to their importance. As you mark certain messages as unimportant and others as important, Sanebox learn to do this in your place result (ideal) so is a perfect sorting messages depending on their importance.
Moreover, SaneBox can be treated as a secretary: a "praying" to warn two days, or months, or next week, you reply to a message, or solved a problem, and she does.
Just give it a try and the good part is if you try to convince your friends, you can get free after the trial.