WordPress Backups

I suppose I can just ftp the site folder to a folder on my hard drive, what is the downside to this?

It is incomplete. You may also need to take a backup of the site’s database. A complete backup consists of both files and the database.

What is the best way/software to fully backup a WordPress self hosted site?

I can’t be sure about the best way, but you could use a plugin to automate the backup process. There are tons of plugins available in the official repo.