Did you try exim4? That was pretty good a few years back, but honestly I took the advice to offload to service and don't run a "real" one anymore. I do on my dev box as localhost so I can test authentication scripts and the like but that's all.

Well, for outbound you'd presumably want an "authenticated smarthost" with setup details on your side varying by what mail server you're using locally.

For inbound, you'd presumably want the server using fetchmail or getmail to then push them into your local mailboxes. Should be plenty of documentation on those projects.

There was plenty of documentation, and what I was trying to do was along the lines you mentioned. My problem was that if anything there were too many different moving parts in the software and too much documentation. Individually it was quite clear what each part was supposed to be doing. Collectively, it simply didn't work: messages weren't reliably sent or delivered, sometimes generating various kinds of logs or error messages, other times silently as far as I could tell. The hard part was trying to pin down which part of the system wasn't set up properly, and I simply didn't have and couldn't find the knowledge to solve that problem within a reasonable amount of time.

Given that fundamentally neither email protocols nor mail store structure on a typical Linux box are particularly complicated, and that all of the software I was using was well established and reputable, it was an exceptionally frustrating experience. Someone with more skill than me would surely have installed the relevant half dozen or so packages from the distro, edited a few configuration files to set up the remote mail server details and identify the local processes to each other, and had everything working within a few minutes. Unfortunately, without that knowledge the sheer number of options and possibilities was overwhelming and I never got that far. What I really needed was a one-page HOWTO for the most simple use case and a setting for each package that said "don't try to do anything clever or unusual", but what I had at the time was literally hundreds of screens' worth of detailed parameters and config file options, each written according to the conventions and assumptions of their own package.

Why don't you just download your mails from your provider via getmail or the like?

I could, but the object of the exercise was to be able to fetch the mail to a local server and then access it from any device on my network (including potentially from a mobile device via VPN). I also wanted to do things like spam filtering and automatically filing incoming mail according to various rules, the same as I'd do with a standalone mail client, and sending all outgoing mail via a system that could keep copies. This is well beyond the scope of running something like fetchmail on its own.

Most email clients allow the user to configure a separate outbound email server.