We study theoretically the different transport behaviors and the electrical characteristics of a top-gated graphene field-effect transistor where boron nitride is used as the substrate and gate insulator material, which makes the ballistic transport realistic. Our simulation model is based on the Green's function approach to solving a tight-binding Hamiltonian for graphene, self-consistently coupled with Poisson's equation. The analysis emphasizes the effects of the chiral character of carriers in graphene in the different transport regimes including the Klein and band-to-band tunneling processes. In particular, the Klein tunneling is shown to have an important role on the onset of the current saturation which is analyzed in detail as a function of the device parameters. Additionally, we predict the possible emergence of negative differential conductance and investigate its dependence on the BN-induced bandgap, the temperature, and the gate insulator thickness. Short-channel effects are evaluated from the analysis of transfer characteristics as a function of gate length and gate insulator thickness. They manifest through the shift of the Dirac point and the appearance of current oscillations at short gate length.