Thin Zn coatings are widely used to protect steel from corrosion like hydrogen embrittlement. Despite its economic importance, the behavior of H in Zn coatings is not well studied. Here, we investigate the H-trapping energies at different defect sites in Zn such as vacancies, Frenkel defects, substitutional atoms, grain boundaries, and microvoids using DFT, and compare them to 9 other metals in bcc, fcc, and hcp crystal structure. As the only metal, Zn repels H at all investigated defects, while Ti shows strong attraction to H. A close look at the band structure of cells with H-defects reveals that as the only investigated metal, Zn does not form localized bonds with H, despite evident charge transfer, explaining the trends in the H-trapping energies. With this knowledge, we next develop machine-learned force-fields for H-diffusion studies using molecular dynamics (MD) for Zn and Ti. Training forces are consecutively sampled from ab-initio-MD simulations of defect cells with several dispersed H atoms, achieving training errors below 0.1 eV/Å, sufficient to perform simulations in poly-grain structures.