We derive a detailed analytical tight-binding (TB) model for a double helix emulating DNA with one type of nucleotide pair and a single oriented π orbital per base. The TB model incorporates both kinetic and intrinsic spin-orbit (ISO) contributions as well as Rashba-type interactions coupled to an external electric field along the axis of the double helix. The helical structure of the molecule renders the ISO first order in the interaction strength (in the meV range) as in carbon nanotubes. The coupling between the ISO and the chirality of the molecule is manifest in the effective coupling parameters while the Rashba coupling is only weakly dependent on structural chirality. A continuum model at half filling is derived where the dispersion is linear around the Fermi level. Spin transport can be completely solved in the case of ISO and the dominant Rashba type term. Spin selectivity is shown to exist for this minimal model (with features similar to recent experimental findings) when the double helix is biased and thus time reversal symmetry is broken. The model also display robustness toward scattering because of the chiral nature of the eigenstates.