To the OP, I didn't see whether you wanted to focus on moving or stationary cars, but it does sound like you're trying to learn. As such, I strongly recommend a DSLR or mirrorless camera. I know they're not cheap, but neither is film.
As far as focal lengths, how close can you get to the action? My camera (D3500) came with a kit 70-300mm. This range seems to be fine when shooting behind the fence at Laguna Seca or my local kart track. It seems a bit long for autocross, but I still feel it works better than my 18-55.
I started shooting with a Nikon D1H and a 70-200mm 2.8. I don't miss the pro body or lens. A modern consumer camera has such good auto focus and high ISO characteristics that the consumer lenses are more than adequate to do just about anything you want.
Whatever you do, don't let any of that stop you from shooting with what you have. If you can get to a local autocross or drag strip, you will get practice in a virtually identical environment to the challenge. The only difference is the cars will be nicer 
I kid, I kid... But, really, spend some time shooting. It can change the way you see the world in a wonderful way.
What's this "film" you speak of?
At an average motorsports event Mrs Frog may shoot 1,000 frames each day. That would be really expensive with film.
If you want to use film, my suggestion is to practice your skills with digital, then go back to the film.
It takes time to get "panning" down correct. What with different environments, lighting, focal lengths etc.
The trick is to get the car crisp, but the tires blurred, so that it doesn't look like the car is just parked at that point on the track.
I shoot with a Canon 5DIII. I usually bring Canon 24-70 f/2.8 and a Sigma 150-600 f/6.3 to the track. Honestly. By the time I add water and a couple snacks that's about all I can haul for a full day.
I use the 24-70 in the pits and the 150-600 on the course.
24mm
70mm
400mm
For the record: I crop and level almost EVERY image I take. I like to change the aspect ratio. I also tend to use the center focus points because they are the most accurate. Most people don't give a E36 M3 if you cropped, but everyone can spot an image that's not level or something that was chopped off in an image that was shot too tight.
The last two comments are, well, nice? This was more of a "hey motorsport photogs, what focal lengths do you bring with you to shoot events?" thread to get a conversation going. I've shot with a crop DSLR for a long time but I honestly have no time around racing (probably an oddity on this forum).
For the last couple of years I've been playing with film. I toyed with going to the Challenge the last two years but life (and then Covid) got in the way. I don't know what the local motorsports situation is where I currently live and I honestly hope to move again this coming year so I don't know that I'll be taking the time to find out.
