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The ability to prepare molecular ions in selected quantum states enables studies in areas such as chemistry, metrology, spectroscopy, quantum information, and precision measurements. Here, we demonstrate (2 + 1) resonance-enhanced multiphoton ionization (REMPI) of oxygen, both in a molecular beam and in an ion trap. The two-photon transition in the REMPI spectrum is rotationally resolved, allowing ionization from a selected rovibrational state of O2. Fits to this spectrum determine spectroscopic parameters of the O2d1Πg state and resolve a discrepancy in the literature regarding its band origin. The trapped molecular ions are cooled by co-trapped atomic ions. Fluorescence mass spectrometry nondestructively demonstrates the presence of the photoionized O2+. We discuss strategies for maximizing the fraction of ions produced in the ground rovibrational state. For (2 + 1) REMPI through the d1Πg state, we show that the Q(1) transition is preferred for neutral O2 at rotational temperatures below 50 K, while the O(3) transition is more suitable at higher temperatures. The combination of state-selective loading and nondestructive detection of trapped molecular ions has applications in optical clocks, tests of fundamental physics, and control of chemical reactions.