Because surface plasmons can be confined below the diffraction limit, metallic lasers that support plasmonic modes can provide miniaturized sources of electromagnetic waves. Such devices often exploit a multilayer design, in which a semiconductor gain layer is placed near a metallic interface with a gap layer in between. However, despite many experimental demonstrations, key considerations for these planar metallic lasers remain understudied, leading to incorrect conclusions about the optimal design. Here, we pursue a detailed experimental and theoretical study of planar metallic lasers to explore the effect of design parameters on the lasing behavior. We print semiconductor nanoplatelets as a gain layer of controllable thickness onto alumina-coated silver films with integrated planar Fabry-Perot cavities. Lasing behavior is then monitored with spectrally and polarization-resolved far-field imaging. The results are compared with a theoretical waveguide model and a detailed rate-equation model, which consider both plasmonic and photonic modes. We show that the nature of the lasing mode is dictated by the gain-layer thickness. Moreover, by explicitly treating gain in our waveguide model, we find that, contrary to conventional wisdom, a gap layer with high refractive index is advantageous for plasmonic lasing. Additionally, our rate-equation model reveals a regime where plasmonic and photonic modes compete within the same device, raising the possibility of facile, active mode switching. These findings provide guidance for future designs of metallic lasers and could lead to on-chip lasers with controlled photonic and plasmonic output, switchable at high speeds.