Many thanks for the replies, here is an update.

While I was having lunch, "it" happened again. I came back to a black screen. But paying more attention this time, the Mac had not switched itself off, the screen had gone black but the fan could just about be heard to still be running.

I held down the power button and switched it off. Then pushed the power button and it started up again, went to log on screen, and powered up perfectly ok. Hmmm. I think it couldn't wake up from sleep? (I have now set the display sleep for a longer interval...)

Before that, I took screen grabs of the two refurbished iMacs which I mentioned, but do not know how to post screen grabs. Meanwhile, the first vendor whom I have used before, the Monterey has gone, but they're advertising a Ventura for the same price. I had a webchat with a technician there who confirmed that the Montereys have been sold and that the Venturas are the same price of £445. I asked him about Numbers and Pages, saying that according to Apple Support they are installed with the OS. He says my spreadsheets and letters etc. will work fine on Ventura. That's a relief.

Since we had to close our business five years ago, I have no website to maintain; I'm not on social media; I only use this computer for internet research, online shopping, internet banking (essential), budgetary management; emails, photo management (I get photos off the camera to here) and relatively simple stuff like that. Oh there is one card game also. I have no need for massive storage space or all the other whizzy things which come with new computers and do not foresee needing them - hence my aversion to throwing a lot of money at this: indeed £445 seems a lot now that we're retired!

Hope that helps and please reply with any ideas wrt paragraphs two and three. Thanks!