This study examines optimized strategies for the preparation of single molecular ions in well‐defined rotational quantum states in an ion trap with the example of the molecular nitrogen ion N. It advances a two‐step approach consisting of an initial threshold‐photoionization stage that produces molecular ions with a high probability in the target state, followed by a measurement‐based state purification of the sample. For this purpose, a resonance‐enhanced threshold photoionization scheme for producing N in its rovibrational ground state proposed by Gardner et al. [Sci. Rep. 2019, 9, 506] is characterized. The molecular state is measured using a recently developed quantum‐non‐demolition state‐detection method, finding a total fidelity of 38±7% for producing ground‐state N under the present experimental conditions. By discarding ions from the trap not found to be in the target state, essentially state‐pure samples of single N ions can be generated for subsequent state‐specific experiments.