Shutter speed depends on the speed of the cars. (Don't you just love non-answers). Slower the cars => slower the shutter => better the motion blur. Essentially, try and get as slow as you can while keeping the car nice and sharp.
I don't have any experience shooting cars in the evenings. What sort of car racing is it? Short track/quarter mile ovals/sprint cars or longer tracks?
If it's short track stuff then your 70-200 may be enough, although 300mm f/2.8 would be ideal (not that I have one, but one day, one dayyy). The 300 would be great for just about any motorsport.
Hope that helps a little.
Neil