How to do the highest resolution FFT?
The FFT size can be longer than the window size.  For instance you can use audio sample windows of 5512 (about 8 per second) and zero-pad them to length 16384 for each FFT.  If noise level is low enough and the separation between frequency peaks is great enough, the interpolation provided by this zero-padding can provide better frequency estimation and plot resolution.

The "highest resolution" FFT reasonable depends on the signal-to-noise ratio as well as the window length, as after a certain point, interpolation and frequency estimation methods will be affected as much by nearby spectral noise as by the spectral peaks that one is trying to estimate at "high resolution".