You will have a couple of hundred failed SSH login attempts a day from automated ssh bruteforce crawlers. So make sure that your username is unique (in some ways it is more important than your password) and your password is strong (12 character, lower,upper,numbers and symbols) would be my advise. Or better yet disable remote password login altogether and only allow login using ssh keys.
EDIT also run
netstat -an | more
And check what ports on the machine are currently open
port 22 is ssh on all network interfaces, so you will see a line similar to the following
tcp 0 0 0.0.0.0:22 0.0.0.0:* LISTEN
Check what other ports are listening for incoming traffic on your machine, and see if you actually need them, if you don't then disable them.
You might also want to Google "bastille ubuntu" or "hardening ubuntu"
There is no such thing as a 100% secure, all you can do is raise your fence higher and make them stronger than other peoples, and hopefully crackers will leave you alone.
I once setup an OpenBSD machine on the Internet on which I modified the source to sshd and ran this 2nd fake copy on port 22. The machine logged the username and password attempts by the automated bots, they were very basic admin:admin apache:webmaster john:mypassword but that was around 5 years ago.