Two-dimensional (2D) materials have shown outstanding potential for new devices based on their interesting electrical properties beyond conventional 3D materials. In recent years, new concepts such as the valley degree of freedom have been studied to develop valleytronics in hexagonal lattice 2D materials. We investigated the valley degree of freedom of GaX and Janus GaXY (X, Y = S, Se, Te). By considering the spin-orbit coupling (SOC) effect in the band structure calculations, we identified the Rashba-type spin splitting in band structures of Janus GaSSe and GaSTe. Further, we confirmed that the Zeeman-type spin splitting at the K and K' valleys of GaX and Janus GaXY show opposite spin contributions. We also calculated the Berry curvatures of GaX and Janus GaXY. In this study, we find that GaX and Janus GaXY have a similar magnitude of Berry curvatures, while having opposite signs at the K and K' points. In particular, GaTe and GaSeTe have relatively larger Berry curvatures of about 3.98 Å and 3.41 Å, respectively, than other GaX and Janus GaXY.