Gmail offers push email to android phones. Push email is a service that sends mail straight to your phone once it's received in your inbox. If you use the gmail app you will automatically have push email from your gmail inbox, sync times are irrelevant as the mail is sent to your phone as it arrives in your gmail inbox, provided you have auto sync switched on. If you don't want to be notified every time an email arrives in your gmail inbox you can switch off auto sync and just manually sync every time you want to see if there is mail there.
Alternatively you can use the standard mail app and set up an account using the pop3 settings from your gmail account. These are available in the settings in gmail on the web. You can then set the frequency of checks to the server to see if you have any new mail. You need background data transfer switched on for this to work but you don't need auto syncing to be on.
Hope this helps.