It is not clear from your questions if they are related. Why would you want to install two servers on the same hardware? You cannot run them simultaneously. For testing, you could set up a dual boot PC.
The installation document of Fedora Core is available from http://fedora.redhat.com/docs/fedora-install-guide-en/fc4/index.html
If you want to have a proxy server between your PC based browser clients and your internet router, Squid comes with Fedora. Fedora can also act as your firewall and router.
Squid allows you to limit internet access to certain PCs only, or business hours only. You can either allow certain sites, or have a blacklist, and control the type of files people can download, if any.
You would install Samba only if you want your users to use the hard drive of the Linux server as file storage area for your Windows PCs.
When you install your Fedora server, you have a choice of installing a graphical interface or just a character interface.
Because you can administer the server through your browser using Webmin, available from http://www.webmin.com, you do not actually need the graphical interface in your Fedora, unless you want to use it when testing and finetuning the system and later install the server with character mode user interface only.
This means that even an older PC can act as your proxy server, with 256MB of RAM.
For managing the Fedora server from your PC in character mode for small command line tasks you can use PuTTY, from http://www.putty.nl/download.html. File transfers to and from Fedora can be done by using the WinSCP (Secure Copy) client from http://www.putty.nl/download.html. Both PuTTY and WinSCP connect to port 22 SSH, which you have to allow if you turn the firewall on in Fedora.
