I am trying to start a webpage for my dad's business. We can't afford to pay the fees for the common tools that are offered, but luckily i know the basics of html, so I can created my own webpage, but I need to know how to make it so that I am only modifying firewall settings for the windows computer that will be being used to host the webpage, not the rest of the network, since my dad uses a home media server also. Is this possible? I would really like to avoid hosting a webpage on a 3rd party server, but as I have mentioned, security is a high priority for the rest of the network

There are free webhosts to get you started. I personally use them.
Because I really wouldn't recommend setting up a public place anywhere near your own PC.