Doubly-selective channel estimation represents a key element in ensuring communication reliability in wireless systems. Due to the impact of multi-path propagation and Doppler interference in dynamic environments, doubly-selective channel estimation becomes challenging. Conventional symbol-by-symbol (SBS) and frame-by-frame (FBF) channel estimation schemes encounter performance degradation in high mobility scenarios due to the usage of limited training pilots. Recently, deep learning (DL) has been utilized for doubly-selective channel estimation, where long short-term memory (LSTM) and convolutional neural network (CNN) networks are employed in the SBS and FBF, respectively. However, their usage is not optimal, since LSTM suffers from long-term memory problem, whereas, CNN-based estimators require high complexity. For this purpose, we overcome these issues by proposing an optimized recurrent neural network (RNN)-based channel estimation schemes, where gated recurrent unit (GRU) and Bi-GRU units are used in SBS and FBF channel estimation, respectively. The proposed estimators are based on the average correlation of the channel in different mobility scenarios, where several performance-complexity trade-offs are provided. Moreover, the performance of several RNN networks is analyzed. The performance superiority of the proposed estimators against the recently proposed DL-based SBS and FBF estimators is demonstrated for different scenarios while recording a significant reduction in complexity.