Ultrafast electron microscopes with thermionic guns and LaB6 sources can be operated in both the nanosecond, single-shot and femtosecond, single-electron modes. This has been demonstrated with conventional Wehnelt electrodes and absent any applied bias. Here, by conducting simulations using the General Particle Tracer code, we define the electron-gun parameter space within which various modes may be optimized. The properties of interest include electron collection efficiency, temporal and energy spreads, and effects of laser-pulse duration incident on the LaB6 source. We find that collection efficiencies can reach 100% for all modes, despite there being no bias applied to the electrode.