Size of Dataset

There isn't any firm rule to indicate the desirable number of data points for a Fourier analysis. The reason is that both the underlying periodicity (usually unknown in advance) and noise affect the results. To take a ridiculous and extreme example, only a few data points are enough to reveal a perfect noiseless sine wave. On the other hand, identifying periodicity in noisy data that have a long wavelength might require millions of points (covering several cycles). It's a dilemma. People commonly run Fourier analyses with 50-100 points, but more than that certainly is desirable. In any case, you can always run the analysis on a dataset and use Fisher's test to see if any resulting peaks are significant.