Laser-plasma acceleration produces ultrashort, high-brightness ion beams reaching tens of MeV, yet their large divergence and broad energy spread require dedicated capture elements for beam transport. Using laser-accelerated protons from the GSI PHELIX laser to the LIGHT beamline as a reference, we developed a framework to optimize and assess such combined capture and transport systems, with emphasis on injection into conventional accelerators. In addition to our numerical analysis we derive scaling laws linking transmission and chromatic emittance growth to the initial half-opening angle, showing that the present performance is primarily divergence-limited. We also estimate and predict the longitudinal bunch quality and quantify the divergence reduction needed to approach injector-relevant intensities.