A multitude of individuals across the globe grapple with motor disabilities. Neural prosthetics utilizing Brain-Computer Interface (BCI) technology exhibit promise for improving motor rehabilitation outcomes. The intricate nature of EEG data poses a significant hurdle for current BCI systems. Recently, a qualitative repository of EEG signals tied to both upper and lower limb execution of motor and motor imagery tasks has been unveiled. Despite this, the productivity of the Machine Learning (ML) Models that were trained on this dataset was alarmingly deficient, and the evaluation framework seemed insufficient. To enhance outcomes, robust feature engineering (signal processing) methodologies are implemented. A collection of time domain, frequency domain, and wavelet-derived features was obtained from 16-channel EEG signals, and the Maximum Relevance Minimum Redundancy (MRMR) approach was employed to identify the four most significant features. For classification K Nearest Neighbors (KNN), Support Vector Machine (SVM), Decision Tree (DT), and Naïve Bayes (NB) models were implemented with these selected features, evaluating their effectiveness through metrics such as testing accuracy, precision, recall, and F1 Score. By leveraging SVM with a Gaussian Kernel, a remarkable maximum testing accuracy of 92.50% for motor activities and 95.48% for imagery activities is achieved. These results are notably more dependable and gratifying compared to the previous study, where the peak accuracy was recorded at 74.36%. This research work provides an in-depth analysis of the MI Limb EEG dataset and it will help in designing and developing simple, cost-effective and reliable BCI systems for neuro-rehabilitation.