Trapped atomic ions are an ideal candidate for quantum network nodes, with long-lived identical qubit memories that can be locally entangled through their Coulomb interaction and remotely entangled through photonic channels. The integrity of this photonic interface is generally reliant on the purity of single photons produced by the quantum memory. Here, we demonstrate a single-photon source for quantum networking based on a trapped Ba-138(+) ion with a single photon purity of g((2))(0) = (8.1 +/- 2.3) x 10(-5) without background subtraction. We further optimize the tradeoff between the photonic generation rate and the memory-photon entanglement fidelity for the case of polarization photonic qubits by tailoring the spatial mode of the collected light. (C) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement