Having OpenSSH running is pretty much essential for any machines you remote administer. Some things you can do: disable password auth, use public keys. Disallow root logins. Listen on a non-standard port. Configure a hardened "jumphost" as your interface between your machines and the outside world.
Also: SSH is considerably more battle-tested in this configuration. There's a lot to be said for being aligned with how the developers imagine a program is used
Also agreed. I'd trust OpenSSH to do security better than MySQL.