I ended up trying something called GoodSync. Bit of a corny name, but after trying it for a few backup "jobs" I quite liked how it worked.
It was recommended by a photographer who I have been taking advice from (via YouTube event videos) regarding software called Lightroom, which is for organising and adjusting photographs. I liked his general attitude and he is quite a good teacher, in my opinion, so when I found out he uses GoodSync to back up his hundreds and thousands of photographs and general data I thought, "yeah, I'll check that out."
I paid £32 for two licenses (I'm going to use it on my wife's computer too). So, not free, but not all that expensive either.
It has a few bells and whistles but I only use it to create a one way backup. I also don't bother with doing checksum checks and rely on the software spotting differences in date/time stamps. For some reason a lot of my existing backup files had different time stamps... Some out by just a minute or two, some out by a whole hour and some out by random amounts. This meant it took me quite a while to get everything back into sync, but now that is done I can backup any changed files quite quickly.
I have also got it writing a particular set of data to my Google Drive and that works well too.
Should have done this a LONG time ago...
Regarding imaging my system drive... I'm still sitting on the fence about this one. When I imaged my 240gb SSD system drive a couple of years ago Acronis worked fine so I may still use that. First, though I have to go get some more USB3 hard drives.
If my system drive does give up the ghost I may well take the opportunity to install stuff from scratch. Sometimes a fresh install works wonders for blowing the cobwebs out and getting rid of stuff you just don't use anymore.