Several recent works have predicted that unconventional and topological superconductivity can arise in graphene, either intrinsically or by proximity effect. Then, the analysis of the spectroscopic and transport properties in graphene would be a valuable source of information in the study of the emergent superconducting order parameter. Using Green's functions techniques, we study the transport properties of a finite size ballistic graphene layer placed between a normal state electrode and a graphene lead with proximity-induced unconventional superconductivity. Our microscopic description of such a junction allows us to consider the effect of edge states in the graphene layer and the imperfect coupling to the electrodes. The tunnel conductance through the junction and the spectral density of states feature a rich interplay between graphene's edge states, interface bound states formed at the graphene-superconductor junction, Fabry-P\'erot resonances originated from the finite size of the graphene layer, and the characteristic Andreev surface states of unconventional superconductors. Within our analytical formalism, we identify the separate contribution from each of these subgap states to the conductance and density of states. Our results provide an advisable tool to determine experimentally the pairing symmetry of unconventional superconductivity that can arise in graphene.