In regards to the snippet, that is a logrotate config that basically says "Clean out any log files in /usr/local/nagiosxi/var but not if the logfile is empty, and don't alert me if it is missing."
logrotate configs are a bit out of scope for this forum, but a good overview of some things you can do with it is here: http://www.thegeekstuff.com/2010/07/logrotate-examples/
Backups usually have more to do with policy than anything in a lot of places. The usual speech is "Keep copies of your copies, keep at least one offsite in a secure location, be prepared to lose anything you don't back up". As for specifics, it also depends on policy and personal preference. I like to keep a daily, a weekly, and a monthy, but this also depends on what sort of data I am backing up. My music collection doesn't need backing up as often as my codebase, and the music collection takes up more space.
Backup management is truly more of an art than a science.
Nagios daily/monthly/weekly backups
Re: Nagios daily/monthly/weekly backups
Former Nagios employee