Photographing drag races poses one major challenge to the amateur photographer. You will be at a significant disadvantage in terms of shooting location compared to the pros. Next time you are at an event look to see where all the pros are shooting from. Hint, it's not the stands. The pros stand on the track, and most of the published shots are either shot head on, or from ground level next to the cars. Shooting from the stands puts you at a bad angle to the action, and you will likely have to deal with other fans blocking your line of site, or the retaining walls obscuring a portion of the vehicles. You will also be significantly farther away from the action needing longer lenses
That being said, there are two types of shots you can attempt - the takeoff, and the pan shot. The good news is that the equipment requirements are quite low. You'll need a medium length lens - depending on how good your seats are figure ~300mm in 35mm terms. Now the really good news - you don't get much benefit from a fast lens. F5.6? No problem. You are effectively a fixed distance from the cars at all time, so you don't have to worry about focus speed. And for the pan shot you are going to be relying on camera drag to blur the background and not depth of field. For the takeoff shot depth-of-field is a problem but there is often times a saving grace - heat distortion. Any car that runs the 1/4 mile in faster than 7 seconds will produce enough exhaust at the start line to blur a good portion of the background for you.
I shoot with an SLR because that's what I have, but I imagine you could get by with a P&S superzoom pretty well too, as long as it has manual exposure controls