I typically use either the "P" mode or "Sports" mode. Definitely don't use the green square because that will pop up the flash when there is cloud cover, and the camera trying to do the flash before taking the photo will slow it down a lot of course.
As for the focus (on the lens), I have mine set to auto.
I don't think I have mine set to "burst mode", "continuous shooting", or anything that's not the default. I'll have to check when I get home, but basically I have everything (except for the flash) on full auto and the photos are typically very quick and look good.
The main setting that needs to be turned off is the 'power save' mode or whatever it's called that could turn the camera off as you're waiting for the first finisher to come in. Also, if you have a newer camera that has WiFi mode, make sure that is turned off because that will disable the USB connection I believe.
I typically put my camera as far down from the finish line as I can get, and I error on the side of having my camera zoomed out too far than too close.