Mail is driving me nuts ...

Any suggestions for what I could do to fix this? Could it have anything to do with my host server account, which has a storage limit, which I've super-ceded ... but don't care about. If I delete the mail up online on the server, to make space, the server auto-syncs with my Mail app (where I really want to have all my mail stored) and deletes all the mail there too. And I don't want the pain of constantly 'saving' my current incoming Mail to a separate folder so as not to inadvertently loose mail.

Or is this something entirely different?