AnalogKid,a) It doesn't matter what I would select. It's not my project and I have no operating parameters.
b) Since I have no idea what the intended application is, I have no idea.
After seven posts, we still have no idea what you are trying to achieve. We do not know if the white noise bit stream is going to the shift register's data input or clock input. If it is the data input, we do not know the clock frequency. The clock acts as a lowpass filter, significantly altering both the "whiteness" and the randomness of the result. This bears directly on the analog front end design.
Or, the white noise bit stream could be driving the clock input, to randomly (in the time domain) sample some other waveform for some other reason. All of this affects the required bandwidth of the noise source.
Three days, seven posts - not one number.
I wish to make a product that converts the noise from space into binary digits stored in a flash drive. I am looking for people who have experience designing circuits of the kind that can implement the analog part of the product.