For users with multiple devices (such as a cell-phone, a tablet and a desktop computer), this is the recommended way to setup your e-mail accounts.
What to setup
Desktop Computer: Use POP3 with "Leave on Server for 14 days"
Cell-Phone or Tablet: Use IMAP
Webmail: No special configruation needed (It also uses IMAP)
What will this setup do?
When you are at your computer, it will download all the e-mails to your computer using POP3.
When you check your e-mail away from your computer, it will use IMAP to read the e-mail directly on the server, but it won't delete anything.
How to set up your accounts
An article on how to setup your accounts is here.