The incremental hydration of the glycine cation is investigated using an ab initio approach fully correcting for basis set superposition errors and explicitly incorporating electron-correlation effects. Structures with zero to four surrounding water molecules have been determined. It is demonstrated that the successive aggregates follow a Darwinian family tree, the most stable complexes systematically belonging to the same branch of the tree. In strong contrast with neutral glycine, the direct hydrogen bonding to the glycine cation is favored over bridging water structures. The agreement between experimental and theoretical hydration enthalpies and Gibbs free energies is impressive, as ab initio estimates almost systematically fit the experimental error bars. For GlyH+-(H2O) and GlyH+-(H2O) 3, we show that two structures are generated by the experimental setup. The present approach also resolves most of the previous theory/experiment discrepancies and provides patterns for the evolution of the vibrational spectra: a decrease of the hydrogen-bond stretching frequency indicating second-shell water molecules. Additionally, the impact of bulk solvent solvation is investigated, as four discrete water molecules still do not fully hydrate the protonated glycine.