I'll give it a stab:
Your throttle return sring simply helps pull the carb closed. It is up to your idle screw on the carb to keep the idle set correctly. Increase this screw to hold the carb open further when it is forced all the way shut, which will help keep the car from dieing (sic?). This will give you a good idle, now you have to make sure your servo and return spring is fully closing the carb to that idle position.
As for setting your nuetral position, here's what I do. Try to get the servo set to provide ample throw for throttle and brakes, so set the servo horn near perpendicular to the carbs travel when at neutral.
Next, set the carb linkage so that this position will cause the carb to be all the way closed, with a little extra force to help ensure it closes each time you return to neutral.
Lastly, set the brake linkage so that in this same position, you brake is off but close to engaging. (If you want drag brake, set it here to be slightly engaged).
Now everything should be set. Use your transmitter to set the endpoints of travel for throttle/brake.
About your starting. It is ok to put your finger over the exhaust, this builds pressure that forces fuel up the line and into the carb. Once running, there is enough pressur/suction to keep fuel coming without your finger.
However, if this is a new problem, maybe you have an air leak? Check the fuel lines for cracks and make sure it is all tight and secure (is it old, have you ever replaced it?). Also check and possibly seal your carb (search around for how to do this, not too bad).
Hope this helps!