What is the low-pass filter that gives minimal transient response?
As mentioned in the comments there is no unique answer to your question, because you're asking for a contradiction. A good low pass filter (i.e. one with a fast transition between pass band and stop band, and with high stopband attenuation) will exhibit a considerable transient response. On the other hand, a filter with a very smooth step response is worse as a frequency selective filter than other filters of the same order. However, a Bessel filter might be a good compromise between these two conflicting goals. It performs reasonably well as a low pass filter, and it has very little overshoot in its step response.