An IMAP account will delete across all devices connected to them. You cannot alter that. If the issue is with an IMAP account don't delete messages you wish to access later. Simple. Exchange accounts also work more or less the same way (which is what your work account likely is).
POP deleted from the server upon download if the client (app) is set up for that. On the iPhone open the Settings App > Mail,Contacts,Calendars > <the account in question> > and look for settings along the line of mail behavior or server settings. It varies a little from vendor to vendor. Deleting mail from one device using POP typically does not delete from other devices. However, the mail client may be deleting it from the server upon download. that is what you are looking to prevent.
POP is a lousy mail system for managing on multiple devices. I'd strongly recommend getting off of it if possilbe (and getting over deleting email if you actual plan to use it later.
BTW: Understanding WHY is the first step to any intelligent problem solving. If you do not understand why the accounts behave as they do, you likely will never get this situated to your liking.