What does Push do?

If you turn PUSH on, it will continuously look for new emails and will bleep when you get one.

If PUSH is turned off you have to manually check to see if you have new email, or set it to check every hour, 30 min, 15 min etc.

PUSH will do nothing for you. The point of push email is that it is pushed to your phone as soon as it hits your mail server (which is seconds after it is sent). BUT, Push email on iPhone only works with three types of accounts that support Push - MobileMe, Yahoo Mail, and MS Exchange/ActiveSync (usually corporate email accounts). No POP accounts support Push, nor does AOL.

So, turn Push OFF, and set Fetch to 15 minutes (the shortest interval).

iphone manual page 104:

"Fetch New Data
This setting lets you turn Push on or off for MobileMe, Microsoft Exchange, Yahoo!
Mail, and any other “push” accounts you have configured on iPhone. Push accounts
automatically deliver new information to iPhone when new information appears
on the server (some delays may occur). You might want to turn Push off to suspend
delivery of email and other information, or to conserve battery life.
When Push is off and with accounts that do not support push, data can still be
“fetched”—that is, iPhone can check with the server and see if new information is
available. Use the Fetch New Data setting to determine how often data is requested.
For optimal battery life, don’t fetch too frequently. "

http://manuals.info.apple.com/enUS/iPhone_UserGuide.pdf