After one of your daily sessions, just pipe the output of
history | cut -c 8- to a file and then clean it up.
history | cut -c 8- > dailystatuscheck.sh
You'll want to add redirects to append any output from each individual command into a file and then and then add a line to email the file to yourself. Then simply add the script you created to cron.daily after testing it.
grep ERROR *.log
df -h >> /tmp/$$.log
cd /var/log >> /tmp/$$.log
grep ERROR *.log >> /tmp/$$.log
mail -s "Daily Status" firstname.lastname@example.org << $$.log
If you are feeling particularly lazy (one of the virtues of a good programmer ;-) add some processing to determine if action is needed. i.e. If free space is less than 90% alert you immediately or mark the email urgent.