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Non-Gaussian operations have been shown to enhance the fidelity of continuous variable quantum teleportation. However, a disadvantage of these non-Gaussian operations is that they are probabilistic in nature. In this article, we study the trade-off between teleportation fidelity and success probability for optimal performance of the teleportation protocol, which to the best of our knowledge, has never been studied before. To this end, we first derive a unified expression for the Wigner characteristic function describing three non-Gaussian states, photon subtracted, photon added, and photon catalyzed two-mode squeezed vacuum states. We then utilize it to obtain the fidelity of teleportation for input coherent and squeezed vacuum states using the aforementioned non-Gaussian resource states. We optimize the product of the relative enhancement in fidelity and the probability of state preparation by tuning the transmissivity of the beam splitters involved in implementing non-Gaussian operations. This leads to a scenario that can be effectively implemented in a lab to enhance fidelity. It turns out that among all the considered non-Gaussian resource states, the symmetric one-photon subtracted TMSV state is the most advantageous. We provide the associated optimal squeezing and beam splitter transmissivity values for the considered non-Gaussian resource states, which will be of significant interest to the experimental community. We also consider the effect of imperfect photon detectors on teleportation fidelity. Further, we expect the derived Wigner characteristic function to be useful in state characterization and other quantum information processing protocols.