In the late 70's-early 80's I was able to get full access photo passes to the USGP at Watkins Glen as my father was the main motor sports writer for Sports Illustrated and he'd get me on their credentials list. At the time I had only a 50mm and a 135mm lens but I think I was able to get some pretty decent photos with just those two focal lengths. Unfortnately I've lost most of those prints and negs over the last 30 years.
My main advice would be to not get into the mindset that you need a fast shutter speed to get good pictures of fast cars. The blurred background/sharp car shot is got by panning with a shutter speed of less than 1/focal length. Standing just past the apex of a corner on the inside of the track is a great place to get shots of drivers at work (especially in open cars).
The other main piece of advice I have for shooting anywhere near the track is KEEP YOUR EYES AND EARS OPEN. If a car loses it and you're in the way you have to be prepared to move FAST!