For one player and a dedicaced windows xp x64, 512Mo is sufficient (you will need a 2GB swap file at least), as the GS really need only 300MB of ram to run (the rest is probably only used as cache or as room to do fast memory allocation, which will never happen if you are alone on your server).
The GS use 2,5GB of ram freshly started with one player logged on, but I don't know how much ram is used per players (for test purpose, I use a server with 512MB of ram actually, 1024 is better but there is almost no difference from the client perspective, it's better if you need to do something else at the same time as the server is running, but I am the only one to log on this server) 8GB for a server should be fine for a small lan server indeed