Machine learning (ML) techniques are increasingly being applied to establish correlations between input parameters and key process responses in the wire arc additive manufacturing (WAAM) process. Despite their potential, there remains limited understanding of how to develop an integrated ML framework that simultaneously considers both the dataset characteristics and the modeling approach to ensure accurate and reliable predictions. The present study addresses this gap by developing an integrated ML framework to predict the deposition behavior of Inconel 625 in WAAM. To capture nonlinear system behavior, three ML methods, namely artificial neural network (ANN), support vector machine (SVM), and adaptive neuro-fuzzy inference system (ANFIS), were developed and systematically evaluated for predictive modeling and process optimization, considering deposited geometry, area, and efficiency as the key output characteristics. The input parameters, i.e., voltage, wire feed rate, torch travel speed, and shielding gas flow rate, were identified as critical factors influencing the deposition process. The datasets were preprocessed to remove noise and analyzed to extract relevant features that captured the intrinsic physical behavior of the process. Performances of the ML models were evaluated using a separate test dataset, and predictions were assessed through mean absolute percentage deviation (MAPD). Results demonstrated that integrated ML framework could accurately represent intricate interdependencies among process parameters on deposition outcomes, providing a robust method of predictive modeling and parametric process optimization for Inconel 625 deposition by WAAM process. The ANN model demonstrated satisfactory performance for forward modeling with MAPD values of 12.24, 14.87, and 11.91 for deposition geometry, deposition area, and deposition efficiency, respectively. For inverse modeling, the ANN accurately predicted key inputs from outputs, with MAPD values of 1.39, 18.91, 12.25, and 19.36 for voltage, wire feed rate, torch speed, and shielding gas flow rate, respectively. Bidirectional predictive modeling keeps to set operating conditions to achieve desired depositions and process automations.