In addition to what everyone else mentioned, all the filtering you need will be accomplished by the ADC itself, and by post-processing the data in software. As a starting point, I'd consider connecting the ADC inputs as "directly" to whatever it is you're measuring as possible - this will remove a whole bunch of design risk. If, in the end, the sensitivity is too low, you can always add external amplification - that may improve S/N ratio but does so at the expense of other parameters.
The reason I am seeking precision is because I expect to need to accurately measure very low currents
The number of bits determines dynamic range. What is the dynamic range of currents you'll be measuring?
All you need in your application is maybe 1% accuracy and 0.1% resolution. A 12-bit ADC is plenty for that, if the range is fixed.
Soil impedance measurements allow for error correction when done across a range of frequencies, and DC is a bad idea due to galvanic effects. When using DC, in order not to degrade the sensing cell, you may need to drive a certain amount of charge into the cell, then reverse polarity and extract that same charge, and so on. The net charge after a measurement session should be zero. This should be fairly precise, as the errors accumulate, and will cause a DC drift. That's why AC impedance spectrum may be less of a chore to obtain.