  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.
