Backing up MySQL database I have quite large and rather important DB to backup.

First off, whats best way to do it?

Secondly, easiest way I know is to export it through phpmyadmin, but, i'm worried about options, although I'm quite sure this "Add DROP DATABASE" will not drop actual databases, I'm interested what are these options for? (see pic)

Thanks.
The best (and IMO the only suitable) tool for backuping a MySql database is mysqldump

The PhpMyAdmin options you are referring to are meant only to alter the generated statements in your dump (but will not touch your actual data). You might want to refer to this FAQ at PhpMyAdmin.