Logwatch
Logwatch is a tool that sends you really nice summary reports of your system logs. The default configuration works pretty well out of the box, once you've set your email address.
Basic Configuration
Copy the default config:
cp /usr/share/logwatch/default.conf/logwatch.conf /etc/logwatch/conf/
Comment out everything you don't want to change. Replace root with your email address in the MailTo directive.
You'll now get daily reports.
Reducing the Frequency
To only get weekly reports, override the Range directive:
Range = between -7 days and -1 days
And move the cronjob to the weekly directory:
mv /etc/cron.daily/00logwatch /etc/cron.weekly/
Note: The range directive is documented, and you can get to the documentation typing
logwatch --range help