Recently, wearable mobility monitoring devices have gained a great deal of attention for collecting movement and gait-related data. Moreover, Wearable movement monitoring devices together with machine learning techniques have been shown to be successful in a variety of healthcare applications, including diagnosis, prognosis, and rehabilitation. However, advanced studies are needed to create accurate and robust models that can differentiate between different populations based on their mobility signatures. This is particularly critical for monitoring movement and gait patterns of individuals impacted by neurodegenerative conditions such as Parkinson's Disease (PD). In order to achieve this goal, it is critical to employ a robust approach to model available data and identify the optimal set of movement parameters for the classification process. In this work, we propose a computational approach to identify the best feature selection method for spatiotemporal gait parameters. We investigate several feature selection approaches and analyze their performance as related to the mobility classification problem; including maximum information gain with minimum correlation (MIGMC), maximum signal to noise ratio with minimum correlation (MSNRandMC), genetic algorithms (GA), decision trees (DT) and principal component analysis (PCA). These methods, along with new proposed variations, are assessed in terms of classification accuracy, the number of selected features, and computation time. Data collected from the triaxial accelerometers attached to the ankles of individuals with PD, geriatrics (GE), and healthy elderly (HE) were used to train and test a set of six different machine learning techniques. Our results indicate that three out of six feature selection methods, including GA, MSNRandMC, and a modified version of MIGMC are the best performers regarding the classification accuracy. We also show that higher degrees of robust performances are achieved when employing multiple algorithms, such as decision trees and genetic algorithms. This study provides a critical first step towards the much-needed goal of utilizing data collected from wearable devices to extract important information for the diagnosis and rehabilitation of many movement-related medical conditions.