Best program to backup Android phone data?

I need a recommendation for a good (free) program which would backup (almost) everything on an android phone (like making Windows Image with e.g. Acronis True Image), which would save everything on PC (or SD card). I'm not a fan of the native Google’s backup system, as it backups to a cloud, and is not very complete in my opinion.
I wish a program, that will, on my request, backup on my PC:
-All current Android system settings
-All installed apps
-All apps data
-All contacts
-All messages
-etc...

And on, my latter request, from such an "image" of the system, could restore any of these individual types of data...

While I used Nokia, it had a very good program called PCSuite (installed on PC), which would do that exactly and perfectly...
Now I'm looking something similar for Android smartphone