Searching for nearby habitable worlds with direct imaging and spectroscopy will require a telescope large enough to provide angular resolution and sensitivity to planets around a significant sample of stars. Segmented telescopes are a compelling option to obtain such large apertures. However, these telescope designs have a complex geometry (central obstruction, support structures, segmentation) that makes high-contrast imaging more challenging. We are developing a new high-contrast imaging testbed at STScI to provide an integrated solution for wavefront control and starlight suppression on complex aperture geometries. We present our approach for the testbed optical design, which defines the surface requirements for each mirror to minimize the amplitude-induced errors from the propagation of out-of-pupil surfaces. Our approach guarantees that the testbed will not be limited by these Fresnel propagation effects, but only by the aperture geometry. This approach involves iterations between classical ray-tracing optical design optimization, and end-to-end Fresnel propagation with wavefront control (e.g. Electric Field Conjugation / Stroke Minimization). The construction of the testbed is planned to start in late Fall 2013.