trough ssh when you connect to your machine run :
lastb -10
This will show you the last 10 login failed attemps you can change to 20 or whatever
you can also run: last -10 to see the last successful logged in
use :
more history
to see all the commands that someone have typed
on the dir /var/logs you have a lot of another logs too
for more paranoid level use
netstat -a
This will show you all incoming and outgoing communications
and like the others said considere using firewall and fail2ban
Note: don’t relly to much on firewalls since they are easy to bypass
keep all softwares updated
read frequently about new vulnerabilities if there is some vulnerability that affects your software until gets patched turn of that service.
Avoid Docker as much as possible. It gives you a quick way to run apps, but in a way that you can’t see what is going to be installed.
It is also double resource heater.
And it has many frequent vulnerabilities.