the fast shutter speed/small aperture advice is pretty failsafe if you just want to capture the car, but if you're after a more dynamic shot i'd also try panning, which involves moving the camera with the subject at a fairly low shutter speed - 1/50 or slower is probably best, though the slower it is the harder it becomes to pull off. takes practice but is fun and useful! if you get it right the subject should be in focus with everything else blurred to emphasise the motion.
this isn't great but is the most recent example i could find on my blog - took it a couple of weeks ago. 1/50, f/5.6, 28mm, ISO 100.
you after a compact, SLR, rangefinder etc?
it might be worth getting a holga or something just to get used to the whole process and come up with very obviously non-digital results. my first film camera was a holga 135 and i love the little guy.
another great camera is the vivitar ultra wide & slim, also made by superheadz with other names such as eximus, UWS, etc...should be about $30 new at the most (mine came free with a magazine here)
mine looks like this but it comes in a thousand different colour variations. it has a 22mm lens (which is equivalent to 14.5mm on a crop DSLR, so it's really wide) and gets awesome results (if you like vignetting and slightly weird colours, at least):
this is the one camera i always, without fail have in my bag. weighs nothing, costs nothing.