first you must know what game will you be serving and the files that game server has to have installed, its not something like download this supports all the games, no, you must know the game server required files and in them you will notice if you need Windows or Linux.
second, are you planning on running the server just LAN or on the Internet too? If in the lan then you must configure your lan for that with some router no need of buying a broadband. The problem comes if planed to serve to the internet too, then you must have a fast UPLOAD bandwith check that with your ISP and that they assign you a PUBLIC IP. As I have said before my ISP has an ip for several computers ¬¬ so I cant put a server, but is the only broadband service offered in here. check that carefully dont want to end setting and Internet Server and all the problem comes from your ISP