Photoelectron photoion coincidence (PEPICO) spectroscopy could become a powerful tool for the time-resolved study of multi-channel gas phase chemical reactions. Toward this goal, we have designed and tested electron and ion optics that form the core of a new PEPICO spectrometer, utilizing simultaneous velocity map imaging for both cations and electrons, while also achieving good cation mass resolution through space focusing. These optics are combined with a side-sampled, slow-flow chemical reactor for photolytic initiation of gas-phase chemical reactions. Together with a recent advance that dramatically increases the dynamic range in PEPICO spectroscopy [D. L. Osborn et al., J. Chem. Phys. 145, 164202 (2016)], the design described here demonstrates a complete prototype spectrometer and reactor interface to carry out time-resolved experiments. Combining dual velocity map imaging with cation space focusing yields tightly focused photoion images for translationally cold neutrals, while offering good mass resolution for thermal samples as well. The flexible optics design incorporates linear electric fields in the ionization region, surrounded by dual curved electric fields for velocity map imaging of ions and electrons. Furthermore, the design allows for a long extraction stage, which makes this the first PEPICO experiment to combine ion imaging with the unimolecular dissociation rate constant measurements of cations to detect and account for kinetic shifts. Four examples are shown to illustrate some capabilities of this new design. We recorded the threshold photoelectron spectrum of the propargyl and the iodomethyl radicals. While the former agrees well with a literature threshold photoelectron spectrum, we have succeeded in resolving the previously unobserved vibrational structure in the latter. We have also measured the bimolecular rate constant of the CHI + O reaction and observed its product, the smallest Criegee intermediate, CHOO. Finally, the second dissociative photoionization step of iodocyclohexane ions, the loss of ethylene from the cyclohexyl cation, is slow at threshold, as illustrated by the asymmetric threshold photoionization time-of-flight distributions.