Many studies have attempted to classify small drones in response to threats posed by the technical progress of small drones. Recently, small drones have been classified utilizing convolutional neural networks (CNNs) with micro-Doppler signature (MDS) images generated from frequency-modulated continuous-wave (FMCW) radars. This study proposes a comprehensive method for classifying small drones in real-time using high-quality MDS images and an ultra-lightweight CNN. The proposed comprehensive method comprises an MDS image generation technique, which can improve the quality of MDS images generated via FMCW radars, and the ultra-lightweight CNN with high accuracy performance despite its remarkable lightness. Experimental results show that the proposed MDS image generation technique increases the accuracy of CNNs by enhancing the MDS image quality. This is further verified using the results of uncertainty quantification. The proposed ultra-lightweight CNN significantly decreases the computational cost while achieving high accuracy. Finally, we demonstrate that the proposed comprehensive method successfully classifies small drones from far distances with high efficiency and accuracy: the maximum and average accuracies for classification are 100% and 99.21%, respectively, and the numbers of parameters, nodes, and floating-point operations of the proposed ultra-lightweight CNN are approximately 4.88 K, 21.51 K, and 31.52 M, respectively.