Any voltage input offset will appear as a 'resistance' to the measured current and any input offset current will add to the error. On the other end of the scale, the maximum measurable current will depend on the current output capability of the amplifier. Click on the image to enlarge. One possible circuit is shown above. A1 is an autozero amplifier, this gives very low input offset voltage.
R sets the gain and C helps to filter out any mains pickup.
A2 buffers the output. C can be say 0.1uF polystyrene capacitor. To give a degree of protection against static discharges etc. If you plan to run a number of ZRAs and need electrical isolation use a separate isolated dc-dc converter to power each one. I you can make sense of it you are welcome to plagiarise it.