Breast cancer (BC) is the most frequently diagnosed cancer among women, surpassing all other types of cancer in terms of prevalence. It affects both males and females, but women are at a greater risk of developing it. The lifetime probability of developing breast cancer for women is approximately 1 in 38. The focus of this study is to differentiate between benign and malignant breast cancer tumors using the fine needle aspiration (FNA) signal as the primary source of information. Four deep learning (DL) models, namely long short-term memory (LSTM), Gated recurrent unit (GRU), Deep belief network (DBN), and autoencoder (AE) have been utilized to achieve this goal. The proposed models have been trained and validated using two public breast cancer datasets: the Wisconsin Original Breast Cancer dataset (WBC) and the Wisconsin Diagnostic Breast Cancer dataset (WDBC). To establish a reliable model, three different types of training techniques have been utilized, including the 80:20 split, the 70:30 split, and the k-fold method. The experimental investigation incorporated three different data characteristics, namely balanced, less imbalanced, and extremely imbalanced data. The simulation-based experimental findings indicate that the LSTM model achieves high levels of accuracy, F1-score, and area under the curve (AUC) when applied to the two commonly used datasets. The WDBC dataset yields accuracy, F1-score, and AUC values of 0.98, 0.98, and 0.99, respectively, while the WBCD dataset yields values of 0.99, 0.99, and 1, respectively. These results were obtained using a 3-fold training scheme and balanced data. The LSTM model consistently outperforms the other three models, regardless of variations in datasets, training methods, and changes in data properties. The efficacy of the models can be evaluated by subjecting the deep learning models to bigger and varying degrees of unbalanced data samples, including both balanced and less skewed datasets. To further this study, we aim to explore the effectiveness of DL models in conjunction with an IoT system to improve breast cancer detection accuracy in online mode for patients residing in remote areas.