Effective hydrogen storage is a crucial requirement for harnessing hydrogen as an energy source. Among various storage methods, solid-state hydrogen storage holds promise but necessitates extensive investigation. This study employs density functional theory within the WIEN2k code to improve the desorption temperature and kinetic properties of MgH2 by introducing Be in combination with transition elements (Ni, Cu, and Zn). The gravimetric hydrogen storage capacity for all studied compounds exceeds 6%. Introduction of different transition elements with Be leads to improvements in formation and cohesive energies, as well as in desorption temperature. Mechanical stability, determined through elastic constants, is confirmed for all hydrides meeting the Born stability criteria. Detailed analyses encompass bonding characteristics, shear modulus, bulk modulus, Cauchy pressures, elastic anisotropy, and Vickers Hardness tests. Electronic properties reveal that Mg2BeZnH8 exhibits the semiconductor nature, and properties are further improved by using TB-mBJ approach. Electronic charge density calculations unveil interatomic bonding nature. Numerous previously unexplored thermodynamic aspects of these hydrides have been investigated and are now presented.