How to correctly connect op-amp to ADC
The series R / shunt C serves as both an anti-aliasing filter and also a charge reservoir for the track/hold. This type of A/D converter (SAR or Successive Approximation Register) has an internal switched-capacitor array which is periodically connected to the input pin, to sample the input voltage. Right at the moment it begins tracking the input, there is a disruption as the internal sampling capacitor is not at the same voltage as the input. As long as it reaches the correct voltage before the tracking interval ends, all is well; but a high-impedance source may have trouble with accuracy. This is explained in the 
Maxim Integrated MAX153 datasheet:


  page 10
  Input Current
  Figure 8 shows the equivalent circuit of the
  converter input. When the conversion starts and WR is low, VIN is
  connected to 16 0.6pF capacitors. During this acquisition phase, the
  input capacitors charge to the input voltage through the resistance of
  the internal analog switches (about 2kOhm). In addition, about 12pF of
  stray capacitance must be charged. The input can be modeled as an
  equivalent RC network (Figure 9). As source impedance increases, the
  capacitors take longer to charge. The typical 22pF input capacitance
  allows source resistance as high as 2.2kOhm without setup problems.
  For larger resistances, the acquisition time (tP) must be increased.  


So there are several design constraints you need to meet:


sensor source impedance
charge reservoir set by SAR internal sampling array
anti-aliasing cutoff frequency set by RC
minimum acquisition time required for accuracy


The sensor source impedance is the equivalent Thevenin or Norton internal resistance of whatever you're trying to measure. If you had any choice you'd obviously want to select 0 impedance, but a practical sensor always has some impedance. Higher impedance means the signal will suffer more distortion, due to the ADC's input current. Anything over about 6000 ohms should be considered "high impedance". In your case you already have an op amp, which has a fairly low impedance output driver.

The C in the filter should be at least as large as the internal sampling capacitance. More external C means less disruption during the tracking interval. However too high C can also cause ringing, overshoot, or sluggish response.

An anti-aliasing filter is required because any input energy present with frequency > 1/2 sample rate, will still appear in the digitized input -- but there is no way to untangle the aliased frequencies from the fundamental frequencies. Generally the anti-aliasing RC cutoff should have reasonable attenuation at the Nyquist aliasing frequency limit. If there's likely to be a lot of extraneous signal above Nyquist limit, that's going to be more of a concern. If it's inside a quiet, shielded enclosure, you can probably get away with less aggressive filtering.

These constrains somewhat interact; sensor impedance affects the R, the SAR internal capacitance affects the C, and the product RC affects the corner frequency.

To be fair, the MAX153 is a really ancient part with very low resolution, but the same principles apply to any SAR type of ADC.