What's the best band for LPDA antenna?

there are different LPDA frequency ranges. You have to define more exactly what you have.

LPDA is a very performant antenna.
An octave band LPDA may be designed (or found on the market) with very high performances.
A decade band LPDA may be found on the high-end, instruments grade, market at higher cost.
If you are a novice, don't try to design a decade band LPDA