Using a Butterworth high-pass filter together with Fast Fourier transform I have a signal and I'm interested in identifying the dominant frequencies greater than 1/3600 Hz. To do this, I use Fast Fourier Transforms and examine the locations of the peaks in the frequency domain, which reveals that the largest peaks are below this frequency. As a noob, it seems like there are two potential options: 


Simply ignore the FFT results outside my desired range and focus on my region of interest.
Filter the signal (e.g., with a Butterworth high-pass filter) before I perform the FFT. 


What are the pros and cons of these approaches? Is there a third (or fourth, fifth, sixth...) option that is better than both of these methods at achieving my goal? 



Edit:
As the comments say: it really depends on your signals. If the energy in the "don't care" region is significantly larger than the energy at the frequency of interest, it's helpful to pre-filter it first. Otherwise you may see "spectral leakage" of the high energy components into your target area. 

On the downside: the pre-filter will affect the group delay the transient response of your overall system. 

This being said: if the filter is not too steep and the cutoff frequency not too close to your target frequencies, pre-filtering is generally a good idea. The pre-filtering is much cheaper than the FFT, so it have almost no impact on CPU or memory requirements.