Most of us have a setup like this:
Home PC(s) - Router & Firewall - Internet
The home PC's have internal IP addresses, non routable, like in
RFC 1918 (rfc1918) - Address Allocation for Private Internets.
The router box, which in most cases for home use can also act as a hardware firewall (not extremely powerful of course) is the one which gets the external IP address, from the public pool.
If you set up PS on your own PC, and that uses an internal address like 192.168.2.100, you will not be able to allow others to connect to it from the outside without creating a forwarding rule between your PC and the firewall. In other words if your router has an IP address like 80.80.80.80, you would have to create this rule of the router (via a graphical/web interface or directly on it via the firewall rules if you know the syntax) which forwards packets back and forth between 192.168.2.100 and 80.80.80.80 on UDP port 13331 (or whichever your server is set up on). Also, make sure your own PC as well as the router have the UDP port open.
A possible problem might be if you have dynamically assigned IP and it gets changed by the ISP automatically from time to time. I believe DynDNS could help... Be advised though, this is not a service for a server with heavy traffic.
Fair warning: Please make sure you comply with the ABC license, do not use any of the proprietary content in PS to run a public server.