Here's what I do:
I export the whole MODX DB with PhpMyAdmin (selecting DROP TABLE IF EXISTS -- otherwise the default settings) to an .sql file in my web-backups directory. I rename the file to sitename-backup-date.
Then I use cPanel's File Manager. I delete all files in the core/cache directory. Then I compress everything in the MODX root directory into a .zip file named sitename-backup-date.zip and download it to the same directory I downloaded the .sql file to.
To restore, import the SQL file in PhpMyAdmin. Then upload the backup .zip file to the MODX root and uncompress it to that directory.
Still in cPanel, use File Manager to delete any files in the core/cache directory, then log in.
You should be back in business with no need to install any extras -- they should all be there.
FYI, the
SiteCheck extra, though not free, will create the .sql file for you very quickly (and do a lot of other stuff) without having to go through the steps in PhpMyAdmin. You still have to download it, though, if you want a local copy. You may also have to set the path to mysqldump executable if SiteCheck default setting doesn't work.