The key to making amplifiers work is negative feedback. As you noted in your question, open-loop gain is not a "good" parameter because it varies too much. However, the open-loop gain of most op-amps is too high to be usable anyway. By a happy conincidence, both of these problems can be solved with negative feedback.
In the schematic below, the op-amp is set up in an inverting configuration (meaning that that the output gets more negative as the input gets more positive) with negative feedback to produce a voltage gain of 100: R2 and R5 form a voltage divider between the output and the input, and the op-amp's inverting input is taken from the divider's output. Note that the gain of this circuit depends almost exclusively on the values of R2 and R5. The values of all other components have a very small effect on the gain. If a positive output, or more gain, is needed, a second inverting amplifier stage can be attached to the output of the first.
In your question, you state
gain is a direct function of the values of resistances (which vary largely!)
I'm not entirely certain what you mean by this, but I think there are two possibilities:
- That the values of the feedback resistors vary, and that this will affect the amplifier gain.
- That the value of your current shunt resistor (the transducer) will vary, and that this will affect the amplifier gain.
In the first case, I don't think I would say that even cheap resistors have a large variation, but perhaps your application is different, and you need gain stability measured in parts-per-million. If you do need such stable gain, I would suggest reading some of the Jim Williams application notes published by Linear Devices (linear.com), which contain a lot of good information about making gain-stable amplifiers. Linear also makes some components (the famous LTC1052 op-amp, for example) that have a very small temperature coefficient and supply voltage coefficient. They also make matched resistors (matching better than 25 parts per million, depending on how much you're willing to pay) on a chip.
In the second case, I think you're misunderstanding the negative feedback network. As long as the output impedance of the transducer is "much" less than the input impedance of the amplifier, the gain of the amplifier does not depend on the impedance of the transducer. In this case, the amplifier has an input impedance of at least 10k Ohms, and the transducer certainly has an impedance of less than an Ohm (note that the value of the current shunt resistor is not the same thing as the transducer impedance). This factor of 10,000 difference certainly qualifies as "much" greater.
simulate this circuit – Schematic created using CircuitLab