Modern day 1/4 mile tracks only record your time once you have moved and broken the beam (same as @ Inters). So (like you say) you can sit there and go when you are ready and still record a good time..
60ft times are all to do with your launch. People who are into drag racing will concentrate vastly on this, as it has a big impact on your final ET (time). Every 1/10th second gained on your 60ft time is generally doubled by the end of the strip (so will be 2/10th quicker).
4WD cars and best with 60ft times, then RWD then FWD (same as on the road). But once slicks are involved, they can all take massive amounts off your 60ft time..
HTH