My question would be, how many times a day does someone try to break into your system ?

If you don't know the answer then maybe you should be running a firewall.

It really depends on whether your network is secure or not, usually what secures your network is a firewall. If that's the one on your router then that should be enough.

Looking in your log files for strange IP's and failed password attempts will let you know if people are trying to get in, if you're running a web server look in the error logs for attempts to access non existing files, usually a bunch from the same IP.

Windows may have more vulnerabilities, but they will still try to break into Linux systems.

Search and read about fail2ban, that's one tool to use when you need to have a service open to the internet.

Hope this helps