You can do it easily enough. I wouldn't advice a VPS, but instead a dedicated server. Even better: have it at your own home or office! You only need a fixed IP address for that. (Already a majority of systems on the Internet are using IPv6, soon you'll easily have fixed IP addresses, because you'll be working only in IPv6.)
Now, the administrative workload of maintaining a mail server is not enormous, but it's bothering, since it looks like the big mail companies keep inventing new systems and protocols (to "fight spam" so they say), so you would have to track all those new stuff and update your configuration.
Basically, talking to other fellow programmers with postfix is easy; talking to customers who use gmail is harder; talking to accountants and bankers who use Microsoft Outlook is hard. You will also have to configure imap and smtp with SSL/TSL (thankfully, nowadays there's letsencrypt.org to provide certificates for free).
And clamav or spamassassin are direly inefficient at modern spam filtering AFAICS. If you want spam-free email, it's Sisyphe-like fight every day.
So it's possible, but you will have to attend to problems from time to time, and it will hard to reach the same level of "quality" as gmail. On the other hand, if you run your email server at home, (or on a dedicated server at a trustable hosting), and use SSL/TLS for all your email connections (smtp-smtp and imap), then you will be able to exchange email in a private and secure way between other people doing the same. Of course, this will be lost as soon as somebody in the mail list is on gmail, or forward to somebody on gmail...
I'd say it's worth it, but it is a little tiring. For example, last month I had to spend a week changing courier-imap for dovecot, just because an update of courier-imap on my debian system broke sasl authentication. This kind of thing tend to occur at the worst time. But this has to be accepted if you don't want all your email read by all the spies and advertisers of the world...