Where to put low-pass filter on the analog signal path?
You might have to put one before the op-amp and one before the ADC. The one before the ADC cleans up line noise as well as op-amp noise as well as performing a certain amount of alias reduction.

The one before the op-amp stops EMI getting in and upsetting the op-amp into producing false dc offsets (it's called input RFI rectification) - see this.

You might have to do some filtering in the MCU too but, a little bit of noise can be a good thing - see dithering

You might also need a low pass filter at the probe and this depends on how well the probe copes with noise at its power terminals (if it has any).

If the probe has an earth connection you might also need to consider isolation methods to avoid ground loops. There are plenty of things that may be relevant.