How to decide to cuttoff frequecies of filter in case of using ADC( Flow: Analog-signal to ADC to bits to fir_filter to filtered_output)
There are a couple of reason's you will see a lot of noise with this circuit:


No anti-aliasing filter. You HAVE to put an analog filter (even a simple RC filter) before the ADC to filter out frequencies higher than your nyquist frequency. If you don't do that, noise on these higher frequencies will alias down to every other frequency you look at and mess up your signal.
You are using a differential ADC but you are not putting in a differential signal (you just tied the negative pin to your voltage reference). Also, almost every differential ADC requires that the average of the voltages at the +/- pin ALWAYS fall within a small range, and your ADC is no different (the ones I've worked with just go haywire if you don't). Look at the datasheet for your ADC. Figure 48 has a setup identical to what you are trying to do -- use that setup and you'll be fine


One last note, as a direct answer to your question, selecting a frequency for your filter completely depends on the frequencies you are interested in. True noise is "white" and will have components across all frequencies. The best you can do is to filter out every frequency you are not interested in to get rid of as much noise as possible. If that's not good enough, you have deeper problems.