There is no one 'best' way to back up. In fact, most sites benefit from using multiple backup methods. Here are my own personal ideas on backup.
I consider 2 'classes' of backup: 'Full site' and 'Database'.
Full site backup is appropriate when changes are made to WordPress, themes, plugins, or uploads. For many sites, this will be done on an 'as needed' basis. These backups are typically large and cannot be emailed to the admin, but must be downloaded or copied using file transfer.
Database backup is needed when new Posts, Pages, Comments, or other content is added to the site. These backups are often done on a regular basis and can be emailed to the admin.
I usually try to use a plugin for backups. In some cases, there are hosting restrictions that make it necessary to use the host control panel, especially for the full site backups.
I often use BackUpWordPress for full site backups. It seems to work on most of the hosts that I deal with.
I usually use either WP DB Backup or WP DBManager for database backup.
Backup is a complicated area. What works for one site may not work for another. If these plugins will not work for your site, there are many others, including paid services that can do it all for you.