This paper presents the development and evaluation of a custom Convolutional Neural Network (CustomCNN) created to study how architectural design choices affect multi-domain image classification tasks. The network uses residual connections, Squeeze-and-Excitation attention mechanisms, progressive channel scaling, and Kaiming initialization to improve its ability to represent data and speed up training. The model is trained and tested on five publicly available datasets: unauthorized vehicle detection, footpath encroachment detection, polygon-annotated road damage and manhole detection, MangoImageBD and PaddyVarietyBD. A comparison with popular CNN architectures shows that the CustomCNN delivers competitive performance while remaining efficient in computation. The results underscore the importance of thoughtful architectural design for real-world Smart City and agricultural imaging applications.