I am working on calculating the homo lumo band gap of some compounds for catalytic protein-ligand using 6-31G basis set. However, I find some of the papers using 6-31G(d) and 6-31G(d, p). Which basis set is most efficient for better calculation?
There is no such a thing as "the best basis set". You must try the largest, most complete and therefore most flexible basis set possible according to the computational facilities you have access to. For some people the best might be 6-31g whereas for others might be aug-cc-pCV5Z. If you achieve better results with poorer basis sets, caution is advised to hidden details in that problem or maybe measurement problems in the experimental referencie values, because we always expect that, at least in principle, a better (more complete) basis furnish better (more accurate) results.