Without shielding from ambient light you will probably never see the tiny pulse variation voltage. The 10Ω resistor was probably chosen to limit the current to a safe level for the LDR, if the LDR went to a very low resistance if exposed to a bright light.
I personally would not use either of your first two linked circuits, because of the DC coupling. It makes it very difficult to amplify the small pulse signal in the large DC offset of the LDR/resistor half bridge.
What test equipment are you using to look at the pulse from your detector?
ken