I have yet to find a great solution to recommend to clients, so my process is this...
I use
BackupBuddy (by ithemes - affiliate link) to back up my clients complete site and then store the backup online, I then use the plugin
WP-DBManager to back up the database (content) on a regular basis or Backup Buddy with their scheduling (but this is only available for maintenance clients). WP-DBManager backups up the database automatically and can be sent by email or stored online. I often arrange to do maintenance for my clients either monthly or quarterly and at those times do a full back up again to keep the integrity of their sites.
I did find this great post about various other
Wordpress Backup plugins and maybe one of those will do the trick for you.
Another option is you can simply download ALL of the files of your current installation and store them yourself and then do this anytime you make a change to the look of your site and use the plugin I suggest to regularily back up your content.
Hopefully, this information is helpful.