Hmm, tricky. Hopefully someone will be along who has actually done this, but my advice based on what I have seen is:
They move fast, really fast, so the further away that you are the easier the panning will be, for this reason take the 70-300 and use it at the 200-300 range. A tripod probably won't be any use, a monopod might be. The stadium will most likely be floodlit so you should have good light.
You need to think what sort of image you want to create. Do you want to show the speed of the dogs against a blurred background? If so I'd go with a shutter speed of perhaps 1/100th second and try panning (depending on the focal length and how steady you are. If you're unsteady and not using a monopod then maybe go upto 500th second), you can use the widest apperture you have with this technique as the background will be a blur anyway, so I'd choose shutter priority and the lowest ISO that the lighting will allow. If you want to freeze the action you'll need a much faster shutter speed. I'm not sure, but would guess 1000th second would be a good start.
You will need continuous autofocus, unless you want to pre-focus on a point and take the photo of the dogs at this point.
Hope this gives you some ideas before someone comes along who has actually taken dog racing pics!
