Oh frabjous day! Callooh, Callay!
Joy is reasonably unconfined in the household, with the arrival of a new Printer - Epson XP-3200 Expression Home.
Plugged it in connected USB cable, pressed Print and after a little think to itself off it went, and it has a proper on/off button as well!
In other words exactly what I wanted. And it will print a scan itself, if asked, not ask for a 'Remote Printer', and doesn't have to be connected to Wi-Fi all the time, which the HP had to be - that fact was at least part of the problem I was having. That fact was buried deep in the "Instructions" that came with it, but I switch everything off at day's end, and had to effectively re-install the HP every morning.