Gallium nitride (GaN) is a wide bandgap semiconductor with many important applications in optoelectronics, photonics, and both high power and high temperature operation devices. Understanding the surface deposition mechanisms and energetics for different precursors is essential to improving thin-film crystalline quality and growth process requirements for extended engineering applications. Here, we use ab initio calculations to study the reaction mechanisms of GaN thin film growth on (0001) surface from ammonia (NH3) and hydrazine (N2H4), nitrogen precursors, and trimethylgallium (TMG) and triethylgallium (TEG), gallium precursors. We find that the initial dehydrogenation of N2H4 is more facile than that of NH3, at 1.15 versus 13.61 kcal/mol, respectively, and that neighboring adsorbed surface hydrogens reduce the barriers for further decomposition of NH2 and NH. We also find that the growth of nitrogen layers is a reaction-limited process rather than diffusion-limited at low adsorbate coverage. On the other hand, the deposition of Ga on a nitrogen rich surface via TMG is limited by the abstraction reaction of the second methyl (CH3) group in TMG, with a barrier of 42.54 kcal/mol. The mechanisms of adsorption of TMG and TEG are different, whereas TMG dissociatively chemisorbs releasing one methane group, the beta-hydrate elimination (C2H4 + H) in TEG is favored through surface interactions (without chemisorption) at a comparable energy barrier to the first CH3 dissociation in TMG. This does not suggest a more favorable thermodynamic route to low-temperature growth, but it does favor TEG for avoiding the explicit abstraction or insertion of C groups during metalorganic chemical vapor deposition (MOCVD) or atomic layer deposition (ALD) techniques.