Handwriting Recognition has been a field of great interest in the Artificial Intelligence domain. Due to its broad use cases in real life, research has been conducted widely on it. Prominent work has been done in this field focusing mainly on Latin characters. However, the domain of Arabic handwritten character recognition is still relatively unexplored. The inherent cursive nature of the Arabic characters and variations in writing styles across individuals makes the task even more challenging. We identified some probable reasons behind this and proposed a lightweight Convolutional Neural Network-based architecture for recognizing Arabic characters and digits. The proposed pipeline consists of a total of 18 layers containing four layers each for convolution, pooling, batch normalization, dropout, and finally one Global average pooling and a Dense layer. Furthermore, we thoroughly investigated the different choices of hyperparameters such as the choice of the optimizer, kernel initializer, activation function, etc. Evaluating the proposed architecture on the publicly available 'Arabic Handwritten Character Dataset (AHCD)' and 'Modified Arabic handwritten digits Database (MadBase)' datasets, the proposed model respectively achieved an accuracy of 96.93% and 99.35% which is comparable to the state-of-the-art and makes it a suitable solution for real-life end-level applications.