Ah, now I get it: tapes are done for as a backup medium. They are just too small and slow.
I couldn’t be bothered with Amanda, until I found this page, which is brief. It’s a bit boring and involved, but, in fairness, not as boring and involved as setting up a DNS or web server properly. And you get network backup done quickly.
So that’s it, my workstation now backs itself up elegantly to a separate hard drive and I will soon have the Macs, local and remote, using it too, securely.