Which folders should be copied when performing a manual backup?
The /Users folder is the most important, thats where all your personal data is kept.

The items in /Applications folder can always be re-downloaded but won't hurt to back them up too. Pay special attention to the apps that can't be easily obtained by downloading from the Mac App Store or from their web-site, like older version of app, an app no longer available from the developer/publisher or a self build app.