We study the binding of neutral silver clusters, Ag(n) (n=1-6), to the DNA bases adenine (A), cytosine (C), guanine (G), and thymine (T) and the absorption spectra of the silver cluster-base complexes. Using density functional theory (DFT), we find that the clusters prefer to bind to the doubly bonded ring nitrogens and that binding to T is generally much weaker than to C, G, and A. Ag(3) and Ag(4) make the stronger bonds. Bader charge analysis indicates a mild electron transfer from the base to the clusters for all bases, except T. The donor bases (C, G, and A) bind to the sites on the cluster where the lowest unoccupied molecular orbital has a pronounced protrusion. The site where cluster binds to the base is controlled by the shape of the higher occupied states of the base. Time-dependent DFT calculations show that different base-cluster isomers may have very different absorption spectra. In particular, we find new excitations in base-cluster molecules, at energies well below those of the isolated components, and with strengths that depend strongly on the orientations of planar clusters with respect to the base planes. Our results suggest that geometric constraints on binding, imposed by designed DNA structures, may be a feasible route to engineering the selection of specific cluster-base assemblies.