In this paper, we present a machine learning approach that generates a system of driver-centered and roadway type-specific deep neural network models for accurate vehicle speed prediction (VSP) in short and long terms in a future horizon. This research focuses on addressing the following issues, proper attributes and window sizes with respect to the lengths of prediction horizons, impacts of roadway types to neural network models, importance of statistical traffic data, and effectiveness of three deep neural network frameworks applied to the short- and long-term VSP problem. Extensive experiments are conducted using the naturalistic driving trips collected from three different drivers on two different routes covering seven different roadway types. Our research results show that the deep learning models structured around roadway types, trained with driver-centered data using optimal window sizes of historical temporal features, including vehicle speed and traffic flow, are effective in both short- and long-term predictions.