I have multiple email aliases that feed into the same box. I filter messages based on what alias they went through and who sent them. Nearly all messages get automatically marked as read; they're there, but I won't get notifed of them. For a few high priority senders who have my high priority alias, they get the star treatment: notification, star, reminder to reply, etc.

Also, if you filter for the word "unsubscribe," you can cut through a good chunk of low-priority automatic messages.