Here's an update for the automatic updates, geared at CentOS/RHEL only.
Dumitru Ciobârcianu tells us that there is a package for CentOS that already does that, named yum-cron. Thus instead of editing files inside the /etc/cron.daily, you can get away with:
This in turn will create two cron jobs, one daily to do the updates, and one weekly, that will also do cleanup such as:
Furthermore it allows configuration for checking packages, and what not. So definitely on CentOS go with yum-cron, since it's the better alternative.
Thank you Dumitru!
On Debian/Ubuntu there is also a package named cron-apt, but that one by default will do only the update of the package definitions (apt-get update -y) and not the actual upgrade of the system.