Accurate brain tumor classification in MRI images is critical for timely diagnosis and treatment planning. While deep learning models like ResNet-18, VGG-16 have shown high accuracy, they often come with increased complexity and computational demands. This study presents a comparative analysis of effective yet simple Convolutional Neural Network (CNN) architecture and pre-trained ResNet18, and VGG16 model for brain tumor classification using two publicly available datasets: Br35H:: Brain Tumor Detection 2020 and Brain Tumor MRI Dataset. The custom CNN architecture, despite its lower complexity, demonstrates competitive performance with the pre-trained ResNet18 and VGG16 models. In binary classification tasks, the custom CNN achieved an accuracy of 98.67% on the Br35H dataset and 99.62% on the Brain Tumor MRI Dataset. For multi-class classification, the custom CNN, with a slight architectural modification, achieved an accuracy of 98.09%, on the Brain Tumor MRI Dataset. Comparatively, ResNet18 and VGG16 maintained high performance levels, but the custom CNNs provided a more computationally efficient alternative. Additionally,the custom CNNs were evaluated using few-shot learning (0, 5, 10, 15, 20, 40, and 80 shots) to assess their robustness, achieving notable accuracy improvements with increased shots. This study highlights the potential of well-designed, less complex CNN architectures as effective and computationally efficient alternatives to deeper, pre-trained models for medical imaging tasks, including brain tumor classification. This study underscores the potential of custom CNNs in medical imaging tasks and encourages further exploration in this direction.