transfer to new email provider

I'm trying to change my email provider but I don't want to lose my existing emails. I have my own domain name which I use as my Apple ID. I have tried exporting mailboxes and then importing them again just to check that I'm doing it right and my emails are there but they are all marked as unread which isn't the case. Am I doing something wrong or is this something I have to put up with? Is there a simpler way for someone who barely understands what they're doing?!