A central challenge in quantum technologies based on atom-like defects is the efficient collection of the emitter's fluorescence. Optical antennas are appealing as they offer directional emission together with spontaneous emission rate enhancement across a broad emitter spectrum. In this work, we introduce and optimize metal-dielectric nanoantenna designs recessed into a diamond substrate and aligned with quantum emitters. We analyze tradeoffs between external quantum efficiency, collection efficiency, radiative Purcell factor, and overall collected photon rate. This analysis shows that an optimized metal-dielectric hybrid structure can increase the collected photon rate from a nitrogen vacancy center by over two orders of magnitude compared to a bare emitter.