The two key concepts to research on the internet are Wampserver and Lampserver. The final choice for which "distro" you will use, will depend on the capability of your "old pc" and how complicated it gets.
Both the "Wampserver" and "Lampserver" are a collection of software packages that will include Apache webserver, Mysql database server and PHP. The former runs on Windows and the latter runs on Linux. Also, in the case of the latter, you can search for complete solutions that include not only the Lamp server but the Linux operating system as well.
Any of them can be configured to act as a production server which allows people from outside to view websites on your web server.
If you are reasonably comfortable with Linux, then a very good choice would be Turnkey Linux Lampserver. Download the ISO and create a bootable CD or USB dongle with it (see LiLo). Start your old PC with it and after the installation is complete you will have a Webserver that you can manage with Webmin.
If your old PC already runs Windows, you could download a suitable Wampserver. Good Wampserver distros include Bitnami, Xampp and Wampserver. You will need to match the capability of your PC with the distro. You may need two or three attempts at installing a Wampserver before you find one that suits an "old Pc" - eg 32bit Windows XP.
This information should get you going. You may have more detailed questions in the future.