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Strontium titanate (SrTiO$_{3}$, STO) stands out as a promising material for various electronic applications thanks to its exceptional dielectric properties. Molecular beam epitaxy is one of the few techniques which allows epitaxial growth of STO directly on industry-relevant silicon substrates. However, maintaining precise stoichiometry and high crystalline quality in this process remains a significant challenge. Establishing this is essential to obtain STO with bulk-like dielectric properties and to minimize leakage current and optical absorbance. In this study, the importance of cationic stoichiometry and the effect of thickness are investigated for STO thin films epitaxially grown on silicon. We employed real-time reflection high-energy electron diffraction (RHEED) as a feedback loop mechanism to counteract Sr source oxidation and maintain a constant flux. Additionally, high-temperature post-growth annealing treatments in O$_{2}$ were investigated to promote layer relaxation and reduce oxygen vacancy concentration, thereby improving the physical, electrical, and optical properties of stoichiometric STO. As a result, high-quality STO thin films exceeding 100 nm were successfully fabricated featuring a bulk-like out-of-plane lattice parameter and refractive index, as well as rocking curve full width at half maximum below 0.2{\deg}, smooth surface (R$_{q}$ < 0.2 nm) and a leakage current density below 1E-7 A/cm$^{2}$., Comment: 16 pages, 8 figures