When you setup your phone, make sure you choose an IMAP account. This way your phone will not download your email, but simple connect to the server and read your mail on the server. This will save room on your phone.
When you setup your computer email (Outlook, Windows Mail, Apple Mail etc.) you should use a POP account. This will download a copy of your mail into your computer so you will always have a copy. You SHOULD go into the Advanced section of your email account settings, and check the box that says “Leave a copy of the email on the server after downloading” You can leave your mail on the server for up to 90 days. So when check your email on your cell phone, you can still read mail that has been downloaded to your computer.