Classifying sleep disorders, such as obstructive sleep apnea and insomnia, is crucial for improving human quality of life due to their significant impact on health. The traditional expert-based classification of sleep stages, particularly through visual inspection, is challenging and prone to errors. This fact highlights the need for accurate machine learning algorithms (MLAs) for analyzing, monitoring, and diagnosing sleep disorders. This paper compares the MLAs for sleep disorder classification, specifically targeting None, Sleep Apnea, and Insomnia, using the Sleep Health and Lifestyle Dataset. We conducted two experiments. In the first one, we selected five key features from the feature spaces using the Gradient Boosting Regressor based on the Mean Decrease Impurity (MDI) technique. We chose two key features using the same methodology in the second experiment. We utilized 15 machine learning classifiers, and Gradient Boosting, Voting, Catboost, and Stacking Classifiers achieved an identical classification accuracy of 97.33%, with Precision, Recall, F1-score of 0.9733, and Specificity of 0.9569 in the original feature space. Among these, Gradient Boosting had the highest AUC of 0.9953 and was 3.36, 5.86, and 20.16 times faster than Voting, Catboost, and Stacking Classifiers, respectively. In the second experiment, the Decision Tree achieved the highest accuracy of 96% in the original and engineered feature spaces and was 149.33 times faster in the engineered feature space. Thus, this research proposes Gradient Boosting as the most effective method, outperforming all state-of-the-art techniques by achieving the highest accuracy, precision, recall, F1-score, and AUC, highlighting its superior classification performance and computational efficiency.