I am new to electronics (this is actually my first arduino project)
It is not an easy project to get working satisfactorily so perhaps you might want to lower your expectations of it or try something more achievable.
While a low pass filter is a good start a simple RC filter is not going to cut it here. You need a filter that drops much more quickly with frequency. This sort of thing is given by the filter's "order" an RC filter is only a first order filter and the output drops with 3dBs per octave. ( An octave is a doubling in frequency and a dB is a deci Bell en.wikipedia.org/wiki/Decibel )
You need a fourth or sixth order filter to get rid of the high frequency stuff. This involves an op-amp for every 2nd order stage and closely matched values of Rs and Cs. So a sixth order filter will consist of three second order stages. Higher Order Filters