(I am an amateur so please be patient with me if I err in my comments.)

In my mind, fastest means to be able to respond to the input signal and faithfully reproduce it at the output, with or w/o gain.  So I would say that slew rate and BW are the main factors in determining the speed of an op-amp.  The problem with GBWP is, even though you can have a really large GBWP, it does not mean your BW is high, and often is the case where a really large gain (low BW) is required to maintain stability.  Therefore if you have a hgh frequency signal other than a fixed sinusoid, the output waveform will experience distortion due to the early roll-off of a high gain, high GBWP opamp.  You'll also have to make sure that your op-amp is capable of driving your load.

The deal here is that, i have developed an algorithm to extract some info which leads me to form an approximation of the impulse response of a circuit, which has a non linear out output.

So by considering a chosen input, we can extract an approximation of the transfer function of the circuit.

The realization of such a circuit, is now a matter of selecting the way to make it, and selecting its components.

I personally, am  not in the field of electronics, so all of my colleagues,  suggest that i should try a passive realization.

Anyway i have been for quite a while now to find a solution to this problem but i have understood that this impulse response is very very fast indeed, so probably, there aren't any opamps so fast, at least not in the present time.

In the attachement i give to you my impulse response function.
The pairing of the nominators with the denominators, is entirely my arbitrary choice!

 Thank you!

thank you very much for your comments!