This is not really a filter but a matching network between the output of the op-amp and the switched capacitor input of the ADC. Its purpose is twofold:
to shield the op-amp from the disturbances of the ADC input sampling transients,
to provide a charge reservoir to refill the ADC input sampling capacitors,
to isolate the channels from each other as the input multiplexer scans them, leaking charge from previous channel to the next one in the scan sequence.
ADC input sampling and multiplexing switching produces very fast transients - they are more in the frequency realm of fast digital edges than what we'd think of as "analog" signals. Those transients are often orders of magnitude shorter than the sampling period of the ADC. E.g. a 100ks/s ADC that samples every 10us and has a 1us sampling gate time, might have transients that last only tens of ns. The more modern the ADC, the faster the transients, as a rule of thumb.
Most affordable op-amps that drive high-resolution ADCs don't nearly have enough bandwidth (or low enough noise) to deal with those transients directly. The op-amp's feedback loop must be thus shielded from the transient, so it doesn't get disturbed and then take "eons" to recover. The sampling capacitors must be also provided a secondary, much faster charge source than the op-amp's output can provide.
There are three time "constants" we need to keep in mind here:
the sampling period - this determines the Nyquist frequency and drives the design of the antialiasing filter,
the sample gate time - the time the sampling capacitor actually samples the input - this determines how quickly the input voltage must settle to maintain full accuracy,
the sampling and multiplexing transient - the time it takes for the impedance stabilization of the CMOS switches used to sample and multiplex the ADC input, as well as the time it takes to precharge the sampling capacitor to the rough neighborhood of the input voltage.
As a rule of thumb, each subsequent time in this list is at least an order of magnitude shorter than the preceding one.
As for choosing the values: absent very accurate models of the parasitics involved, it takes experimentation to select appropriate values. Often there may be two or three disparate combinations of parts that yield equally good performance, e.g. 1nF+20R or 1uF+50R. It is also the case that more such varied combinations work with a faster op-amp, but the slower op-amps won't be able to cope with the "fastest" combinations. E.g. an op-amp substitution may make the 1nF network useless, whereas the 1uF network works for both.