If you have an iPhone the best way to know about new Email is to have a notification pushed to the phone as soon as it arrives.
Apple can do push notifications through the apple servers to any iOS app on the phone that supports it.
The iPhone also supports Microsoft Exchange ActiveSync as a push service, but free services like gmail are dropping support on their free Email service and a lot of the Email services do not have it as a setup option.
Without a push service one option is have the email app fetch new email every 15mins in the email app setting but this wastes battery power when there is no Email to fetch and is not a quick notification like push.
There is an answer for iOS 7 push notification on all email services on the iPhone for all Email accounts and that is a web and app service called PROWL.
In your Email service settings like gmail you can forward a copy of the incoming email to a second email address, if that address is a special email address in the PROWL web service the from address and the subject line of the email can be forwarded through the apple push notification service to the PROWL iPhone app within seconds.
You can download the app through iTunes and the small price is well worth the notification options that can go beyond email.
After downloading go into the iPhone settings and enter the Notification Centre Settings, scroll down to the Prowl.app and make sure the Badge App Icon, Sounds and ALERTS setting is on.
Go into the https://www.prowlapp.com website and Register a username log-in and password, return to the Prowl.app and enter the same log-in into the app to link the app to the website.
Now for the fun part, goto the API Keys page https://www.prowlapp.com/api_settings.php and Generate a new API key with the (Optional) Note [ mail ].
This will make a API Key and an API Email Address that looks like this [ 6cff5*******API-KEYemail@example.com ].
A test Email to this Address will make a Push Notification on the iPhone with the from-address, subject and body of the Email.
A modified version changing [ ..@api.prowlapp.com ] to [ ..+firstname.lastname@example.org ] as shown here https://www.prowlapp.com/prowlmail.php will remove the body from the email used as a notification.
The Email Address now looks like this [ 6cff5*******API-KEYemail@example.com ] this is the Address to forward a copy Email too in your web-based email service like gmail to notify the arrival of new Email for the phone.
The Email fetch setting on the phone can now be set to [ 1 hour ] or [ Manually ] to save on battery life.