First you need a destination for the backups. Let's say it is /backup. It says "important files" and to me that means you pick and choose. For example, out of /etc, maybe passwd, shadow, group, and hosts. There are probably others but all of /etc sounds excessive. Any of /opt also sounds excessive to me. Once the script is working you can tweak the exact file list. Also the exact list will vary from OS to OS and you haven't told us yours.

So it sounds like you cd to /backup, create etc, cd to /backup/etc and copy the files you pick from etc. And repeat this for other directories that have file that you feel are important. cp has an exit status and you will need to check it to see if the cp was successful.

The script should be run out of cron.

I think that this should give you enough ideas to start your script.