With a console login, you are for all intents and purposes physically at the server. Most hosted solution provide a web based interface to simulate this type of behaviour.
I usually immediately install fail2ban,
sudo apt-get install fail2ban
You don't need to know what it does right away (other than it blocks a user from logging for a period of time after too many incorrect passwords) but it makes your box much safer.
If your system is on the Internet and you only have SSH login with a user name and password, make sure it is strong. Your password can be broken in within minutes.
You also want to go straight to SSH RSA Key Based Authentication.
Synchronize Server Time
The ntp daemon calculates the drift of your system clock and continuously adjusts it.