Thyroid disease is an endocrine illness that is defined by the thyroid gland failing to produce enough hormones. Additionally, it is critical to identify thyroid disease early so that medical professionals may develop more suitable treatment plans and prevent major consequences. In this study, four classifiers—Naive Bayes (NB), logistic regression (LR), K-nearest neighbor (KNN), and decision tree (DT), with and without feature selection strategies were used to construct machine learning models for thyroid disease prediction. The data were gathered via Kaggle. Principal component analysis (PCA) and linear discriminant analysis (LDA) were used as feature selection techniques to enhance the model's performance and high data complexity. The confusion matrix, accuracy, precision, recall, and F1 score were used to evaluate the models. According to the results, KNN with PCA was the most accurate model, with an accuracy of 99.3%, whereas naive Bayes with LDA was the best at achieving a compromise between speed and accuracy, with an accuracy of 95.5%. The logistic regression was equally consistent relative to the other parameters, underscoring the necessity of helpful feature values. This study demonstrates how PCA effectively reduces dimensionality and how feature selection is equally important in medical machine learning. Most significantly, these findings point to naive Bayes with LDA as the quickest diagnostic option and KNN with PCA as the most accurate method. For medical professionals, this study is quite helpful. This study helps to overcome gaps in existing diagnostic procedures by enhancing prediction approaches.