In medical research and clinical practice, Bayesian survival modeling is a powerful technique for assessing time-to-event data. It allows for the incorporation of prior knowledge about the model's parameters and provides a more comprehensive understanding of the underlying hazard rate function. In this paper, we propose a Bayesian survival modeling strategy for proportional hazards regression models that employs the Sine-G family of distributions as baseline hazards. The Sine-G family contains flexible distributions that can capture a wide range of hazard forms, including increasing, decreasing, and bathtub-shaped hazards. In order to capture the underlying hazard rate function, we examine the flexibility and effectiveness of several distributions within the Sine-G family, such as the Gompertz, Lomax, Weibull, and exponentiated exponential distributions. The proposed approach is implemented using the R programming language and the STAN probabilistic programming framework. To evaluate the proposed approach, we use a right-censored survival dataset of gastric cancer patients, which allows for precise determination of the hazard rate function while accounting for censoring. The Watanabe Akaike information criterion and the leave-one-out information criterion are employed to evaluate the performance of various baseline hazards.