This work focuses on the design of a deep learning-based autonomous driving system deployed and tested on the real-world MIT Racecar to assess its effectiveness in driving scenarios. The Deep Neural Network (DNN) translates raw image inputs into real-time steering commands in an end-to-end learning fashion, following the imitation learning framework. The key design challenge is to ensure that DNN predictions are accurate and fast enough, at a high sampling frequency, and result in smooth vehicle operation under different operating conditions. In this study, we design and compare various DNNs, to identify the most effective approach for real-time autonomous driving. In designing the DNNs, we adopted an incremental design approach that involved enhancing the model capacity and dataset to address the challenges of real-world driving scenarios. We designed a PD system, CNN, CNN-LSTM, and CNN-NODE, and evaluated their performance on the real-world MIT Racecar. While the PD system handled basic lane following, it struggled with sharp turns and lighting variations. The CNN improved steering but lacked temporal awareness, which the CNN-LSTM addressed as it resulted in smooth driving performance. The CNN-NODE performed similarly to the CNN-LSTM in handling driving dynamics, yet with slightly better driving performance. The findings of this research highlight the importance of iterative design processes in developing robust DNNs for autonomous driving applications. The experimental video is available at https://www.youtube.com/watch?v=FNNYgU--iaY.