What is best practice to remove static noise?
The standard method to remove stationary noise is spectral subtraction, where
the magnitudes of the short-time Fourier transform of the noisy signal are modified based on an SNR estimate in the respective frequency bin. The algorithm by Ephraim and Malah (see this paper) and its variants are used a lot. Note that the basic principle of spectral subtraction is very simple, but that a lot of engineering is necessary to make it sound good. A very important ingredient is the noise/SNR-estimator.