Breast cancer, a significant threat to women's health, demands early detection. Automating histopathological image analysis offers a promising solution to enhance efficiency and accuracy in diagnosis. This study addresses the challenge of breast cancer histopathological image classification by leveraging the ResNet architecture, known for its depth and skip connections. In this work, two distinct approaches were pursued, each driven by unique motivations. The first approach aimed to improve the learning process through self-supervised contrastive learning. It utilizes a small subset of the training data for initial model training and progressively expands the training set by incorporating confidently labeled data from the unlabeled pool, ultimately achieving a reliable model with limited training data. The second approach focused on optimizing the architecture by combining ResNet50 and Inception module to get a lightweight and efficient classifier. The dataset utilized in this work comprises histopathological images categorized into benign and malignant classes at varying magnification levels (40X, 100X, 200X, 400X), all originating from the same source image. The results demonstrate state-of-the-art performance, achieving 98% accuracy for images magnified at 40X and 200X, and 94% for 100X and 400X. Notably, the proposed architecture boasts a substantially reduced parameter count of approximately 3.6 million, contrasting with existing leading architectures, which possess parameter sizes at least twice as large.