  We introduce the PBW degeneration for basic classical Lie superalgebras and
construct for all type I, $\mathfrak{osp}(1,2n)$ and exceptional Lie
superalgebras new monomial bases. These bases are parametrized by lattice
points in convex lattice polytopes, sharing useful properties such as the
integer decomposition property. This paper is the first step towards extending
the framework of PBW degenerations to the Lie superalgebra setting.
