© 2018 IOP Publishing Ltd and Sissa Medialab. The CMB Stage 4 (CMB-S4) experiment is a next-generation, ground-based experiment that will measure the cosmic microwave background (CMB) polarization to unprecedented accuracy, probing the signature of inflation, the nature of cosmic neutrinos, relativistic thermal relics in the early universe, and the evolution of the universe. CMB-S4 will consist of O(500,000) photon-noise-limited detectors that cover a wide range of angular scales in order to probe the cosmological signatures from both the early and late universe. It will measure a wide range of microwave frequencies to cleanly separate the CMB signals from galactic and extra-galactic foregrounds. To advance the progress towards designing the instrument for CMB-S4, we have established a framework to optimize the instrumental configuration to maximize its scientific output. The framework combines cost and instrumental models with a cosmology forecasting tool, and evaluates the scientific sensitivity as a function of various instrumental parameters. The cost model also allows us to perform the analysis under a fixed-cost constraint, optimizing for the scientific output of the experiment given finite resources. In this paper, we report our first results from this framework, using simplified instrumental and cost models. We have primarily studied two classes of instrumental configurations: arrays of large-aperture telescopes with diameters ranging from 2-10 m, and hybrid arrays that combine small-aperture telescopes (0.5-m diameter) with large-aperture telescopes. We explore performance as a function of telescope aperture size, distribution of the detectors into different microwave frequencies, survey strategy and survey area, low-frequency noise performance, and balance between small and large aperture telescopes for hybrid configurations. Both types of configurations must cover both large (∼ degree) and small (∼ arcmin) angular scales, and the performance depends on assumptions for performance vs. angular scale. The configurations with large-aperture telescopes have a shallow optimum around 4-6 m in aperture diameter, assuming that large telescopes can achieve good performance for low-frequency noise. We explore some of the uncertainties of the instrumental model and cost parameters, and we find that the optimum has a weak dependence on these parameters. The hybrid configuration shows an even broader optimum, spanning a range of 4-10 m in aperture for the large telescopes. We also present two strawperson configurations as an outcome of this optimization study, and we discuss some ideas for improving our simple cost and instrumental models used here. There are several areas of this analysis that deserve further improvement. In our forecasting framework, we adopt a simple two-component foreground model with spatially varying power-law spectral indices. We estimate de-lensing performance statistically and ignore non-idealities such as anisotropic mode coverage, boundary effect, and possible foreground residual. Instrumental systematics, which is not accounted for in our analyses, may also influence the conceptual design. Further study of the instrumental and cost models will be one of the main areas of study by the entire CMB-S4 community. We hope that our framework will be useful for estimating the influence of these improvements in the future, and we will incorporate them in order to further improve the optimization.