The circuit from that last link is the TIA circuit. The current is flowing through the resistor in the feedback path of the OP. So there is no voltage amplification, but the OP works as a buffer and suppresses the burden voltage, so that one can use a larger resistor. The input terminals are the far left of the 1 st. circuit part. However this only the very basic circuit, without protection and it may oscillate with a capacitive source. So the pA meter thread is probably the better starting point - there should be protection parts included.
If just the µA range and no need to worry about pA's the choice of OP is relaxed quite a bit.
The shunt + amplifier circuit is good for high currents like 1 mA and up. Though it still works for lower currents, down to maybe 10 pA resolution.
The TIA circuit can work down to very low currents, but is limited at higher current like more than 1-10 mA, as the amplifier must provide the current and due to self heating at that higher current.
While the shunt circuit kind of needs a low offset (e.g. AZ type) amplifier, the TIA type circuit can get away with a more normal OP, as the offset is relative to the output voltage range, so something like 10 or 100 times less important.