300-400 meters is too far away for decent pictures -- you'd need something like a 1200mm lens to get about a 10-meter field of view (which is a lot if you're shooting cars anything but side-on). And acquiring and tracking a moving target with a lens that long is nothing like fun, not to mention the difficulty involved in getting saturated colours at that distance (you'd need to do some post-processing -- haze will suck more life out of the colours than you can imagine if you're not in the desert).

You should be able to get a pass that lets you get into the marshals' area if you ask ahead of time and make it clear that you're there for photography rather than entertainment. That will let you use lenses that are considerably smaller, lighter and more agile. You'll probably still find a good use for a 70/80-200mm zoom (perhaps with a teleconverter) if you're working the corners or hills. The faster, the better if you're shooting cars head-on or tail-on -- for passing shots, you can rely on panning to make the car(s) sharp and the background blurred, but when the cars are moving almost directly toward or away from you, you'll need to rely on a limited depth of field. If you don't own such a lens, you can rent.

You will probably find less use for a wider lens except at the start and finish, but bringing a normal zoom (moderate wide to moderate tele) will cover that if you need it. If you're shooting static vehicles, something on the wide side (16-18mm) will usually add more visual interest than a normal or tele length. Again, whatever you have for a normal zoom will probably cover the territory at the wide end.