Using Lanczos exact diagonalization, we investigate the effects of the competition between the electro-electron and electron-phonon interactions in the context of the 1-D tight-binding Peierls-Hubbard Hamiltonian, studying various structural, optical, and vibrational properties of strongly correlated systems. We use polyacetylene as our experimental guide, and perform a parameter space search to determine the level at which a unique set of parameters can model this prototypical conducting polymer and, more generally, the applicability of the simple'' 1-D Peierls-Hubbard Hamiltonian to these highly interesting materials. 9 refs., 3 tabs.