Selection of suitable glass composition for vitrification of high-level radioactive wastes (HLWs) is one of the major challenges in nuclear waste reprocessing. Atomic and molecular level understanding of various structural, thermodynamical, and dynamical properties of a glass matrix can help in preliminary screening and thus reduce the dependency to some extent on tedious experimental procedures. In that context, extensive molecular dynamics (MD) simulations have been performed to calculate various microscopic properties of the glass matrix. The present article demonstrates that the "Buckingham potential-included long-ranged Coulomb interaction" can be utilized to simulate the glasses of varied compositions. The proposed simulation model has been validated for a wide range of glass compositions: pure glass matrix-SiO2 and B2O3; binary glass mixtures-SiO2-B2O3, Na2O-SiO2, and Na2O-B2O3; ternary glass-Na2O-SiO2-B2O3; and also the Cs2O- and SrO-doped matrix of sodium borosilicate. Most importantly, the MD results have been validated with those of in-house synthesized glasses. The effect of alkali addition on the density and network connectivity of the glass matrix has been explored. The results capture well the boron anomalies for varied concentrations of network formers and network modifiers. The intermediate structural ordering in glasses has been explored by calculating the partial and total structure factors. Further, the characteristic vibration density of states of constituent atoms in the glass matrix is determined. In addition, the glass structures with the addition of dopant oxides Cs2O and SrO have been examined as they are known to be prime heat-generating agents in HLWs. The results establish the structure and dynamics of the doped glass matrix to be a complex nature of the dopant's mass, concentration, charge, and ionic radius. The present MD results might be of great academic and technological significance for further studies in the field of vitrification and prediction of effects associated with the dopant's nature and concentration.