The problem you raised is called spectrum estimation, when trying to using fft to visualise the signal frequency you are performing non parametrical estimation. When you increase the number of points in the fft you increase the resolution in this way the plot appear to be more dense, the drawback is when you have frequencies to close, when you dont know the frequency content of the signal it is hard to decide if what are you seeing is frequency content or spectrum leakage, in order to minimize the efect of spectrum leakage you can use windows techniques, using for example , barlet, blackman or kaiser windows, usualy you will perform trial and error untill you got a reasonable result, nom parametrical spectrum estimation is sometimes refered as an art since there are no defined steps to follow...