We classify the finite-dimensional representations of the Lie superalgebras ${\rm osp}(3,2)$, $D(2,1;\alpha)$ (the one-parameter family of deformations of ${\rm osp}(4,2)$) and $G(3)$. In short, indecomposable representations in the non-trivial blocks are, up to isomorphism and duality, naturally parametrized by positive roots of an infinite Dynkin diagram of type $D_\infty$ or $A^\infty_\infty$. From this result we can deduce the representation type of all basic classical Lie superalgebras but $F(4)$.