A lower ISO is less sensitive to light, but gives a clearer image so it's best for daylight, a higher ISO is more sensitive, but (with film) grainier or (digitally) noisier, so it's better for dusk or indoor photos. 400 is kind of unacceptably noisy on the G6 though there is software that can clean it up a bit. I'd say try 100 or 200 for the game, and use a tripod if possible, the low light and tele lens will be conducive to camera shake. Your built-in flash will probably be useless, turn it off.
You want to shoot with the lowest ISO possible. In bright daylight, ISO 50 is always great, but if you don't have the light, you'll probably need to use a higher speed if you hope to stop motion. (You could shoot with longer exposures and a tripod, but the players on the field would be streaks of color) I'd use a tripod anyway, it almost always makes for better photos.
Bryan