Using SSMTP and configuring it like COPS:config_local.php lets me mail OK!
I'm not 100% satisfied with how (it mail as root [in the mail from: field] and I do not like that, but changing this via "revaliases" does not seem to work.
Further I am looking into the packages
mailutils and
heirloom-mailx and figuring out which one is best to install.
Thank you for your links, they put me on the right track.
Edit: problems with heirloom-mailx (for now). Solving them is a nice task for tomorrow. Never mind, FIXED (typo

)
And fixed my first "problem" with SSMTP as well for the most part. I can live with this.