The rapid growth of the field of time-resolved and ultrafast electron microscopy has been accompanied by the active development of new instrumentation. Recently, time-resolved microscopes equipped with a field emission gun have been introduced, demonstrating great potential for experiments that benefit from the high brightness and coherence of the electron source. Here, we describe a straightforward design of a time-resolved transmission electron microscope with a Schottky field emission gun and characterize its performance. At the same time, our design gives us the flexibility to alternatively operate the instrument as if it was equipped with a flat metal photocathode. We can, thus, effectively choose to sacrifice brightness in order to obtain pulses with vastly larger numbers of electrons than from the emitter if for a given application the number of electrons is a crucial figure of merit. We believe that our straightforward and flexible design will be of great practical relevance to researchers wishing to enter the field.