Arduino logging vertical acceleration data
Yes, you need a time reference. A timer interrupt which sets off the ADC conversion is usually the best bet. Its also possible to let the ADC free-run and use periodic (every n-th) reading. That makes for OK time data, if not great. 

As for the frequency of sampling, what you need to figure out is the bandwidth that you need. Suppose the vibrations that ensue are have a frequency of x Hz, you would need atleast 2x Hz to reconstruct a vibration assuming its purely sinusoidal. This is sort of a theoretical limit. Since a pothole isn't going to produce a sinusoidal vibration, and theory doesn't always translate directly to real life, you'd probably need to sample at atleast 10x Hz. 

For something like a car, I would guess the vibrations to be in the order of, say, 10Hz to 1KHz. (For reference, buildings generally vibrate at sub 1-Hz. Small metallic objects designed to withstand vibration and things like rockets would vibrate in the 50-200 Hz range. Tuning forks vibrate at Kilohertz, usually , like the 32.768 KHz tuning forks commonly used in electronics for time keeping, and quartz crystals vibrate in the MHz range). So a sampling rate of above 10KHz is porbably more than enough. You could try with less and see if it works, but I really haven't done any calculations for cars to be sure. I'm fairly confident 1KHz should be as far as the vibrations should go, and it'll probably be less than than in reality.  

EDIT : If you're only really interested in the large scale vibration of the car, as you say 10-13Hz is what you are interested in, 100Hz should be enough. I'd sample at 1KHz to be safe.