In this work, we address the phenomenon of charge transport in DNA using a simple, but chemically specific, approach that is intimately related to the Su-Schrietfer-Heeger (SSH) model. The emerging potential energy surface for hole transport is analyzed using Marcus' theory of charge transfer. Our results are fully compatible with the conjecture of charge transfer in DNA via two competing mechanisms, and the computations provide the corresponding charge-transfer rates both in the short-range superexchange and in the long-range hopping regime as the output of a single atomistic theory. Finally, the model allows the computation of the transport properties of systems containing modified bases and of more complex arrangements of base pairs as an additional element of verification.