The majority of the proposed graphene-based THz devices consist of a metamaterial that can optically interact with graphene. This coupled graphene-metamaterial system gives rise to a family of resonant modes such as the surface plasmon polariton (SPP) modes of graphene, the geometrically induced SPPs, also known as the spoof SPP modes, and the Fabry-Perot (FP) modes. In the literature, these modes are usually considered separately as if each could only exist in one structure. By contrast, in this paper, we show that even in a simple metamaterial structure such as a one-dimensional (1D) metallic slit grating, these modes all exist and can potentially interact with each other. A graphene SPP-based THz device is also fabricated and measured. Despite the high scattering rate, the effective SPP resonances can still be observed and show a consistent trend between the effective frequency and the grating period, as predicted by the theory. We also find that the excitation of the graphene SPP mode is most efficient in the terahertz spectral region due to the Drude conductivity of graphene in this spectral region.