how to selective push notification iphone

If you use push email to be notified of incoming email, but hate being notified about "unimportant" email, there's a trick where you can have only "important/urgent" email (or whatever you specify) be pushed. It's a great way of reducing interruptions, and also possibly increasing battery life.

The trick here is to have two email accounts:

1. A "main" email account. This is the account you use to send/receive mail, and is the address that you give out to people. The one big requirement here is that the email service must support server-side filtering and email forwarding via filters. Google's gmail supports this, but it's not the only one.
   
2. A push email account. You can use any push email account for this.

The idea here is that you set up server-side filtering on your main account to only autoforward the "important" messages to your push email account. When an "important" message is received, your mail account autoforwards it to your push email account, which causes your iPhone to beep/vibrate. If a regular message is received, it's not autoforwarded, and nothing happens on the iPhone.

The only real downside is that, if your iPhone is connected to both accounts, some mail gets duplicated. However, I just periodically do a "delete all" on the push account, and just read/write email from the other account.