The magnetic ground state and the hyperfine coupling parameters of some first-row transition metal (TM) atoms (Ti, Cr, Mn, Fe, Co, and Ni) adsorbed on ultrathin insulating oxide films are studied by means of DFT calculations. The results obtained using GGA, screened hybrid, and GGA+U functionals are compared for TMs adsorbed on free-standing MgO(100). Then, the case of adsorption on MgO mono- and bilayers supported on Ag(100) is studied using GGA+U. Along with the problematic aspects inherent to the calculation of hyperfine coupling constants, a critical dependence on the magnetic state and electron configuration of the TM is reported, which implies a real challenge for the state-of-the-art DFT methods. In the cases where all functionals considered provide a coherent magnetic and electron configuration, however, the calculated hyperfine parameters do not depend significantly on the choice of the functional. In this respect, the role of the metal support in the hyperfine coupling constants is highly system-dependent and becomes crucial in all cases where the support modifies the oxidation state of the adatom, induces a change in the bonding site or simply induces a rearrangement of the orbital energy diagram. This has important implications for the modelling of single TM atoms deposited on insulating ultrathin films supported on metals for application in quantum technologies or as memory devices.