Make a full back up of the sites including:
All web site files on the server
The database in full
Upgrade to the latest WordPress version ensuring that the site design and functionality stays intact
Repairing of anything broken in the theme if needed after upgrade
Updating of all plugins to the latest version
Secondary complete back up of web site after upgrade including:
All web site files on the server
The upgraded database in full
Upgrading of Events calendar plugin for the migration of data storage to an upgraded system server side