The mysqldump command will output a text file that is an SQL script for restoring the database. You can use mysqldump in a script launched using cron if you leave the system running.
The text file can be zipped.
Remember that the least reliable part of a computer system is the one between the chair and the keyboard. You are far more likely to accidentally delete data than lose it because of hardware failure. For that reason rsync is pretty useless as a backup tool. Instead use cp with the --backup=numbered parameter. As a rule of thumb don't consider your data to be safe unless you have copies on at least three devices in at least two locations.