But to your questions:
It is not hard to run a mailing list, if you know how to run a mail server, and are familiar with text based config files. Running the mail server and sorting out DKIM SPF DMARC will probably take some research. Dealing with RBLs etc is annoying but can be accomplished if you're on a netblock with a good history. You probably are not though.
Spam is not an issue, if your membership is invited, approved, or moderated.
Mailman is "fine". Set it up once and it works forever. Getting it set up is a fair bit of work, the first time. Mailing lists end up being fairly complicated things, and -- at least as of the last list I ran on Mailman -- these things are not optimized for operator experience.
For a very small and manually curated membership, you could just use an alias on your mail server. Mailing list software just automates sub/unsub actions, digest, archives, etc. You might not need any of that.
These options are either fun projects, or they are headaches, depending on your goals. If the latter, it's infinitely easier to set up Google Groups. When I shut down the last mailing lists on my servers, most of them transitioned to GG and there have been no complaints from the new operators (who were neophytes).
All the usual caveats about Google apply of course. Most people don't care.