BaSn$_2$ has been shown to form as layers of buckled stanene intercalated by barium ions~cite{Kim_2008}. However, despite an apparently straightforward synthesis and significant interest in stanene as a topological material, BaSn$_2$ has been left largely unexplored, and has only recently been recognized as a potential topological insulator. Belonging to neither the lead nor bismuth chalcogenide families, it would represent a unique manifestation of the topological insulating phase. Here we present a detailed investigation of BaSn$_2$, using both {it ab initio} and experimental methods. First-principles calculations demonstrate that this overlooked material is a indeed strong topological insulator with a bulk band gap of 360meV, among the largest observed for topological insulators. We characterize the surface state dependence on termination chemistry, providing guidance for experimental efforts to measure and manipulate its topological properties. Additionally, through {it ab initio} modeling and synthesis experiments we explore the stability and accessibility of this phase, revealing a complicated phase diagram that indicates a challenging path to obtaining single crystals.