A few thoughts:
Do you have your
firewall configured and running? If not, configure it. (Linux firewall capability is built-in; it's called iptables. Linux "firewall applications" are generally utilities to make configuring iptables easier.)
Install
fail2ban; it's in the repos.
If you have not done so, change your router password from the default, then
close any public-facing ports in the router that you do not actively need; consult your router manufacturer's documentation for how to do this. (You should do this in any case, regardless of the OS you are running on your computer.)
A web search for
hardening linux will turn up a number of useful articles.