The rate of the reaction is fastest when $Z$ is:

The rate of nucleophilic acyl substitution depends on the leaving group ability of $Z$. A better leaving group corresponds to a weaker conjugate base.${\text{Cl}}^{-}$ is the weakest base among the options (${\text{Cl}}^{-},{\text{CH}}_3{\text{COO}}^{-},{\text{C}}_2{\text{H}}_5{\text{O}}^{-},{\text{NH}}_2^{-}$).
Thus, acid chlorides are the most reactive toward nucleophilic attack.