By default, when using a POP3 email account, the first device that accesses the email server gets all of the current messages downloaded to it. When a second device accesses this same account, there will be no messages on the server as they have already be downloaded to the first device.
An IMAP email account leaves the messages on the server so that any device can access messages. However, if you delete a message with one device, it is removed from the server and no additional devices can "see" it.
To attempt to meet your goal, you would have to copy messages from the IMAP server to local email folders on the computer so that deleting any from the server (from the phone) would not affect other devices. Not a very efficient way to use email.
If POP3 is not an available option, it may be because the particular email provider you are using does not support this older standard. For example, Apple's iCloud Mail only supports IMAP.