For a weak current signal at 50HZ (peak to peak is probably between 10nA - 100nA), if you want to amplify it to mV level, what op-amp can you use to achieve that?

To handle such a small current, you should use an op-amp with a high input impedance and a low temperature vote. You can just connect an inverting proportional amplifier with such an opamp and take 1 megohm input resistance.

We recommend the OPA333 op amp, which is a rail-to-rail op amp with an output amplitude that is very close to the supply voltage, and is a low-power, low-profile, zero-drift amplifier with ultra-low misalignment (2uV), ultra-low quiescent current (17uA), an operating voltage as low as 1.8V, and SC70 or SOT23 packages, making it ideal for applications such as medical instrumentation, temperature measurement, and test equipment. The OPA333 utilizes TI's high-performance, high-precision mixed-signal CMOS manufacturing technology with auto-zero to provide extremely low offset voltage and near-zero drift over time and temperature. The device provides a high impedance input *** mode range of 100mV, can be used 1.8V (minimum) ~ 5.5V (maximum) single or dual power supply. The OPA333 has an excellent ****-mode rejection ratio (CMRR) and does not suffer from crossover errors like traditional compensated input stages.