Whats the optimal window function to use for analyzing real-time data samples?
A full-width rectangular window (a.k.a no window) would best emphasize spectral content near the edges of an FFT aperture, at the cost of artifacts caused by convolution of the spectum with a Sinc function, also called "spectral leakage".  If you can ignore or compensate for these spectral artifacts then there's little reason to window.

But you might be asking the wrong question.  If you want the fastest possible response to some specific frequency band, you should be using a minimum phase filter (or a bank of them, as needed) or a close approximation to such, not a faster block DFT.  Then you can update with each new sample instead of waiting to process a block, and tune the time-frequency response of the filter(s) for each specific band of interest.