Several concepts now exist for small, space-based missions to directly characterize exoplanets in reflected light. While studies have been performed that investigate the potential detection yields of such missions, little work has been done to understand how instrumental and astrophysical parameters will affect the ability of these missions to obtain spectra that are useful for characterizing their planetary targets. Here, we develop an instrument noise model suitable for studying the spectral characterization potential of a coronagraph-equipped, space-based telescope. We adopt a baseline set of telescope and instrument parameters appropriate for near-future planned missions like WFIRST-AFTA, including a 2 m diameter primary aperture, an operational wavelength range of 0.4-1.0 μm, and an instrument spectral resolution of λ/∆λ = 70, and apply our baseline model to a variety of spectral models of different planet types, including Earth twins, Jupiter twins, and warm and cool Jupiters and Neptunes. With our exoplanet spectral models, we explore wavelength-dependent planet-star flux ratios for main-sequence stars of various effective temperatures and discuss how coronagraph inner and outer working angle constraints will influence the potential to study different types of planets. For planets most favorable to spectroscopic characterization—cool Jupiters and Neptunes as well as nearby super-Earths—we study the integration times required to achieve moderate signal-to-noise ratio spectra. We also explore the sensitivity of the integration times required to either detect the bottom or presence of key absorption bands (for methane, water vapor, and molecular oxygen) to coronagraph raw contrast performance, exozodiacal light levels, and the distance to the planetary system. Decreasing detector quantum efficiency at longer visible wavelengths makes the detection of water vapor in the atmospheres of Earth-like planets extremely challenging, and also hinders detections of the 0.89 μm methane band. Additionally, most modeled observations have noise dominated by dark currents, indicating that improving CCD performance could substantially drive down requisite integration times. Finally, we briefly discuss the extension of our models to a more distant future Large UV-Optical-InfraRed (LUVOIR) mission.