It's probably not the 'best' solution... but as my piggy-bank was sounding a bit hollow (following recent purchases, lol) I decided to go with
this KVM just for the time being. It's by Aten, £36.99.
I figured that it will be better than having to keep shutting-down and swapping connections. Hopefully, it will be okay until funds recover enough to consider a more expensive KVM with DVI, etc.
It was very easy to set up, of course. Monitor, speakers, mouse and keyboard are functioning (albeit that the keyboards internet function keys - for email, browser, etc., no longer work. Bit of a shame, but just a minor thing... I'll just have to get used to clicking again.

)
I can switch between computers simply by tapping
Scroll Lock twice - thought that was rather good. There are other key commands, but I've not experimented with those yet.
Thank you all again for your guidance. It has been an enormous help.
