Parkinson's disease (PD) is a debilitating neurological disorder that necessitates precise and early diagnosis for effective patient care. This study aims to develop a diagnostic model capable of achieving both high accuracy and minimizing false negatives, a critical factor in clinical practice. Given the limited training data, a feature selection strategy utilizing ANOVA is employed to identify the most informative features. Subsequently, various machine learning methods, including Echo State Networks (ESN), Random Forest, k-nearest Neighbors, Support Vector Classifier, Extreme Gradient Boosting, and Decision Tree, are employed and thoroughly evaluated. The statistical analyses of the results highlight ESN's exceptional performance, showcasing not only superior accuracy but also the lowest false negative rate among all methods. Consistently, statistical data indicates that the ESN method consistently maintains a false negative rate of less than 8% in 83% of cases. ESN's capacity to strike a delicate balance between diagnostic precision and minimizing misclassifications positions it as an exemplary choice for PD diagnosis, especially in scenarios characterized by limited data. This research marks a significant step towards more efficient and reliable PD diagnosis, with potential implications for enhanced patient outcomes and healthcare dynamics.