For the purpose of farming drag races you just want the car with the highest acceleration, and a good top speed - handling isn't much of an issue.
for the games you can start with/can buy with In-Game Cash my list would be :
E class - Volkswagen Scirocco (best acceleration of all starting cars, 3rd best top speed, the Dodge challenger and volkswagen R32 have a little bit more top speed, but slower accelleration)
D class - Audi RS4 (best aceleration and speed for it's class, at least when it comes to cars you can buy for in-game cash.)
C class - Audi Quattro 20 V (in-game cash car with thebest acelleration together with the Audi TT RS Coupe, but the Quattro has a bit higher topspeed and much better handling)
B Class - Either the Lamborghini gallardo spyder or Dodge Viper srt10 (i went for the dodge viper since the best A class car is also a Lamborghini)
A class - Lamborghini Murcielago Roadster hands down. (best accelleration/ good top speed and decent handling)