On your phone, you can set it to not show previews or even show up on the screen. It'll show in the mail command center if you use an iphone (i.e. it'll show a number), but it won't display on your phone. If you're interested in that, then I can post directions.
Otherwise, you can create filters in GMAIL, but it won't ding for the specific email (hence why I did the gmail account from the start, but I've also been through this before and didn't want to go through it the same way again).