While I am still looking for a backup solution that works for dummy users, I have found one feature that (apparently) none of the backup+imaging software tools I've found does:
Doing a harddisk image to a NAS drive (and esp. verifying it) takes a long time. Therefore, the best option would be to do this at system shutdown (in addition to any scheduling).
However, none of them appears to be able to:
When a user initiates a shutdown (or hibernate, ...) it opens a friendly Window informing him that a backup (or verification) is still in progress/missing/planned and ask him if he want's to run this now and shutdown the PC afterwards.
I find this requirement very natural, so I'm wondering whether I'm missing something in the tools or maybe this ain't technically possible with Windows (XP through 7) or whatnot ...
Note: I simply will not use online solutions for doing full disk images, therefore I haven't even looked at cloud backup tools.