Greetings,
This is not quite correct as stated; the 2.2mV/amp figure represents a sensitivity figure/coefficient, hence 0A*2.2mV/A=0mV. The expression of your data logger’s input character doesn’t seem quite right to me, so I might suggest a careful reading of those specs also.
The “gain” figure you’re referencing would be “open loop” gain, e.g. gain before any feedback is applied. Ideally this figure would be infinite, but it’s not, so it gets characterized because when negative feedback is used to achieve more useful gain figures, the difference between 85dB of open loop gain and 100dB makes a small, but sometimes non-negligible difference.
Analog Devices’ op amp applications handbook is a comprehensive resource on all things op-ampy. The below comes form page 8 of section 1, and is the basic form of the circuit you’ll want.
This thread contains similar information in more condensed form. It needs updating, but might be found helpful. Something like a TLV271CS-13 might be an inexpensive, flexible, and fairly well-rounded choice for many purposes.
Did that too, but then I turned to the dark side…