The increasing penetration of renewable energy sources into the power grid has prompted the development of many energy storage systems, amongst which Adiabatic Compressed Air Energy Storage (A-CAES) is deemed one of the more promising technologies. A-CAES systems can be categorized into solid A-CAES and liquid A-CAES, both of which have received extensive treatment in the literature. In this paper, thermodynamic and economic models are built for each of these systems and their sub-components, and the appropriate materials are selected for the corresponding Thermal Energy Storage (TES). A hybrid TES system is also considered, combining solid TES for low-pressure air with liquid TES for higher pressure. Results for this are compared with the other two systems. Parametric and optimisation studies have been carried out and suggest that the hybrid system has thermodynamic and economic advantages over the other two. The trade off between efficiency and cost and the factors affecting this trade off are also investigated.