Dedicated server automatic backup solution

Actually I'm using rsnapshot for backup. It can't backup mysql db itself, but it allows to execute scripts before and after backup. So before rsnapshot executes:

 /usr/bin/ssh remote_host 'mysql -N -e "SHOW DATABASES;" | while read db; do mysqldump --skip-comments $db |gzip > ~/db/${db}.sql.gz; done'

all mysql settings are stored in ~/.my.cnf and after backup is done rsnapshot executes script to remove dump on remote host.

Also rsnapshot uses hardlinks, when it makes backup, so it saves your space and you have full backup for any moment it was done.

Rsnapshot uses rsync to transfer data, therefore it's more secure then ftp.

We have a similar situation and we use automysqlbackup (instead of mysqldumper as in your case) and rsnapshot as well. Automysqlbackup can inform you as well by email.