Brain tumor diagnosis remains a critical challenge due to the heterogeneity of tumor types and their subtle manifestations in medical imaging. Traditional diagnostic workflows, which rely heavily on manual interpretation, are prone to variability and subjectivity. This study presents a computationally efficient brain tumor detection framework designed for deployment in resource-constrained clinical environments. The proposed approach leverages a pretrained Xception convolutional neural network, fine-tuned on brain MRI scans, to classify tumors in an end-to-end manner. To enhance generalization and robustness, the model was trained and validated on a small-scale dataset (Dataset1) using an a Google Colab accessible T4 GPU, augmented with image transformations, and evaluated on a significantly larger, independent test set (Dataset2). Additionally, we explore a modular extension in which deep features extracted from the trained CNN are classified using conventional machine learning algorithms such as Support Vector Machines (SVM), Random Forests (RF), Decision Trees (DT), k-Nearest Neighbors (KNN), and Logistic Regression (LR), to benchmark performance across models and facilitate interpretable deployment options. The fine-tuned CNN achieved 98% validation accuracy on Dataset1 and 94.7% accuracy on the external unseen Dataset2, demonstrating strong cross-dataset generalization. The hybrid CNN-SVM model attained up to 99.91% accuracy on Dataset1, outperforming the end-to-end configuration in internal validation. This hybrid architecture enables flexible deployment by balancing deep learning accuracy with the simplicity of classical classifiers. Our framework, based entirely on publicly available tools and datasets, offers a scalable, cost-effective, and generalizable solution for early brain tumor diagnosis in resource-constrained healthcare settings.