Motivated by the recent discovery of superconductivity in the iron-based ladder compound BaFe_2S_3 under high pressure, we derive low-energy effective Hamiltonians from first principles. We show that the complex band structure around the Fermi level is represented only by the Fe 3d_xz (mixed with 3d_xy) and 3d_x^2-y^2 orbitals. The characteristic band degeneracy allows us to construct a four-band model with the band unfolding approach. We also estimate the interaction parameters and show that

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... e system is more correlated than the 1111 family of iron-based superconductors. Provided the superconductivity is mediated by spin fluctuations, the 3d_xz-like band plays an essential role, and the gap function changes its sign between the Fermi surface around the Γ point and that around the Brillouin-zone boundary.