Abstract: Linear accelerators provide significant advantages for hadron therapy, including fast energy modulation and reduced activation compared to circular machines. Although Side-Coupled Drift Tube LINACs (SCDTLs) are commonly integrated into the injector designs of such accelerators due to their compactness and efficiency, a detailed and systematic radio-frequency (RF) design and optimization framework focusing on their electromagnetic characteristics, RF efficiency, and achievable accelerating gradients is notably absent in existing literature. This study introduces a thorough approach to the RF design and optimization of a 3 GHz SCDTL structure, presented as a representative study for ion acceleration in medical applications, based on standard design parameters for such systems. By carefully refining the geometry of both accelerating and side-coupling cavities, as well as fine-tuning the coupling system, the work achieves maximized effective shunt impedance and achievable acceleration voltage, while ensuring compliance with limits on the maximum surface electric field and the modified Poynting vector. The findings provide a clear pathway to balance compact design and RF efficiency, contributing to the advancement of practical and high-performance 3 GHz SCDTL implementations in hadron therapy LINACs.