Apache/PHP/Perl all have windows applications, so you should be able to pull this off on the windows machine, if not FC2 is a great choice for an internal server.
First off, running the webserver on an internal ip address shouldn't be an issue, that is configured in the webserver configuration file.
Regarding the domain name; is this going to be accessed from the internet?
If not, you can just buy the domain name and point it to an internal ip address, and configure the virtual host entry in the webserver configuration.
If it is, you will need to have an eternal ip address, the easiest way to get this done is just to map the ip address to the internal ip address. This can typically be done on the ROUTER/NAT whatever you have connecting your internal machines to the internet. Once this is done, just configure the domain's DNS to point to the internet ip address. The downside of this, is if you link to your own site, your machine will have issues processing the request, unless you configure your 'hosts' file to have your domain name mapped to your internal ip address.
Hope this helped, please let me know if you need more help.