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!
Over 20 years ago I was fortunate enough to be invited to the Spa F1 race meeting in Belgium by some people who had spare tickets. We drove down overnight from the UK and arrived at daybreak. At 5am in the morning on the first practice day there was no one about so we drove onto the circuit and did a couple of laps, stopping on pole position of the grid to take some photos and the next time round we pulled into the pits, put the bonnet up, and took a few more pics of our vauxhall estate before going to find the local campsite. After putting our tents up we walked back to the circuit in time for the first practice session. We were directly opposite to the back of the pits before practice and saw a couple of people run across the track into the pits. Not wanting to miss an opportunity, we all did the same and spent the whole of the first practice session in the back of the pits watching drivers come in and out and the mechanics working on the cars. I took of lots of photographs of drivers, cars and mechanics. I was only challenged twice for my pass and luckily the steward spoke no English and I pleaded ignorance and got away with it. I've never been to an F1 race since but can recommend getting a pit pass if you can. Or just learn how to vault a barrier or two:D