PC Dedicated Server
I am using a 600Mhz PIII with 384M RAM with a 5+ Mb/s cable connection as a dedicated server for PS2 and it is working great... very little lag, even for large player numbers. I have it set to the max players, but I have not filled the room yet.
I don't think the speed of the computer matters as much as the pipeline coming into your computer (Internet bandwidth). If I had to guess a formula, I would say that you need 35k/s for each person you want to play on your server.
ie: 16 players would equal roughly 560 kilobytes per second of bandwidth needed.