The recent advancement of deep learning architectures, neural networks, and the combination of abundant financial data and powerful computers are transforming finance, leading us to develop an advanced method for predicting future stock prices. However, the accessibility of investment and trading at everyone's fingertips made the stock markets increasingly intricate and prone to volatility. The increased complexity and volatility of the stock market have driven demand for more models, which would effectively capture high volatility and non-linear behavior of the different stock prices. This study explored gated recurrent neural network (GRNN) algorithms such as LSTM (long short-term memory), GRU (gated recurrent unit), and hybrid models like GRU-LSTM, LSTM-GRU, with Tree-structured Parzen Estimator (TPE) Bayesian optimization for hyperparameter optimization (TPE-GRNN). The aim is to improve the prediction accuracy of the next day's closing price of the NIFTY 50 index, a prominent Indian stock market index, using TPE-GRNN. A combination of eight influential factors is carefully chosen from fundamental stock data, technical indicators, crude oil price, and macroeconomic data to train the models for capturing the changes in the price of the index with the factors of the broader economy. Single-layer and multi-layer TPE-GRNN models have been developed. The models' performance is evaluated using standard matrices like R2, MAPE, and RMSE. The analysis of models' performance reveals the impact of feature selection and hyperparameter optimization (HPO) in enhancing stock index price prediction accuracy. The results show that the MAPE of our proposed TPE-LSTM method is the lowest (best) with respect to all the previous models for stock index price prediction.