The direct detection of sub-GeV dark matter particles is hampered by their low energy deposits. If the maximum deposit allowed by kinematics falls below the energy threshold of a direct detection experiment, it is unable to detect these light particles. Mechanisms that boost particles from the Galactic halo can therefore extend the sensitivity of terrestrial direct dark matter searches to lower masses. Sub-GeV and sub-MeV dark matter particles can be efficiently accelerated by colliding with thermal nuclei and electrons of the solar plasma, respectively. This process is called solar reflection. In this paper, we present a comprehensive study of solar reflection via electron and/or nuclear scatterings using Monte Carlo simulations of dark matter trajectories through the Sun. We study the properties of the boosted dark matter particles, obtain exclusion limits based on various experiments probing both electron and nuclear recoils, and derive projections for future detectors. In addition, we find and quantify a novel, distinct annual modulation signature of a potential solar reflection signal which critically depends on the anisotropies of the boosted dark matter flux ejected from the Sun. Along with this paper, we also publish the corresponding research software.