We carry out a theoretical analysis of factors that dictate the binding affinity and selectivity of the copper efflux regulator (CueR) toward different metal ions (Cu+, Ag+, Au+, Zn2+, and Hg2+). In addition to a simplified active-site model, we have established a computational framework based on quantum mechanical/molecular mechanical (QM/MM) and Poisson-Boltzmann approaches that allows us, for the first time, to systematically analyze the protein contribution to transition metal binding affinity and selectivity. We find that the QM/MM model leads to relative binding affinities that are consistent with observations from transcription induction experiments, while an active-site model does not, which highlights the importance of explicitly considering the protein environment for a thorough understanding of metal binding properties of metalloproteins. Regarding the trends in binding affinity, our analysis highlights both intrinsic properties of a metal ion and protein contributions. Specifically, the softness and desolvation penalty of a metal ion make large contributions to the binding affinity; for example, we find that the large desolvation penalty for Zn2+ rather than any stereoelectronic factor (e.g., linear vs tetrahedron coordination) is the key reason that Zn2+ binds much more weakly than Hg2+ to CueR. Moreover, our results explicitly demonstrate that the electrostatic environment of CueR is well-tuned to favor the binding of coinage metal ions over divalent ions. Finally, our analyses highlight the importance of considering the proper solution reference (i.e., the metal ion bound to buffer ligands vs water molecules) when discussing the binding affinity of metal ions to proteins.