A noble metal nanoparticle (MNP)- quantum emitter (QE) composite nanostructure operates as a nanoscale counterpart of a conventional laser, and serves as an ultra-compact coherent source of surface plasmons, which holds the potential of bolstering device miniaturization. Equivalent to a standard laser, the MNP acts as the resonator, and the gain medium consists of pumped QEs. In this work, we demonstrate the possibility of engineering the emission statistics of such a plasmonic laser, to meet prerequisites set by its intended application. We perform a comprehensive analysis on plasmonic statistics of a spheroidal MNP-QE composite nanostructure, through reduced density matrix formalism, and examine the tunability of the key observable quantities against various system parameters including the geometry of the MNP, the rate of excitation, and the dielectric constant of the submerging medium, to gather the insights for customizing and optimizing this composite nanostructure for a particular application. For a given frequency of operation, our simulations offer a guide for the most suitable shape of the resonator, and provides the estimations for the expected energy output and its coherence, for a range of input power. Furthermore, it can be extended to assist in making the material choices. In essence, our work facilitates tailoring efficient, coherent and tunable plasmonic laser devices to power-up many promising nanoscale applications.