A nightmare over several days. I had set my mind that a local store was no good, because I needed to be able to access my email from outside the apartment, and decided that IMAP would be the way to go.
Technically, what I needed to do was to take the mail I got from my outside provider and download it to my server (this one). Then I needed to pass that email to an IMAP server, finally to get to it from the outside world. This seems stupid at first, but I run a dozen filters on my email, so that it makes very little sense for me to access the email directly on my ISP’s site.