In this and a subsequent article, the range of application for relativistic density functional theory (DFT) is extended to the calculation of nuclear magnetic resonance (NMR) shieldings and chemical shifts in diamagnetic actinide compounds. In the given first paper, various issues are explored that are related to this goal. dt is shown that both the relativistic DFT-ZORA (zeroth-order regular approximation, as developed for NMR properties by Wolff, S. K.; Ziegler, T.; van Lenthe, E.; Baerends, E. J. J. Chem. Phys. 1999, 110, 7689) and the older quasi-relativistic (QR) DFT methods are applicable to these compounds. Another popular relativistic method, the use of relativistic effective core potentials (ECP) for the calculation of ligand NMR parameters, is tested as well. It is demonstrated that the ECP approach is beyond its limits for the very heavy actinide compounds. Comparing the ZORA and Pauli approaches, it is found that Pauli is mon accurate for the H-1 NMR in UF6-n(OCH3)(n) compounds whereas ZORA is more accurate in other cases. This is in contrast to earlier studies that always showed ZORA to be superior. The neglect of spin-orbit effects, leading to scalar relativistic approximations, is possible in some cases. In other cases, however, spin-orbit cannot be neglected. For instance in UF5(OCH3), a large spin-orbit chemical shift of about 7 ppm has been found for the H-1 nuclei but only small effects for the other Ligand nuclei. The large influences of the reference geometry, the reference compound, and the exchange correlation (XC) functional are demonstrated and discussed. The F-19 chemical shift tensor in UF6 is well reproduced by the ZORA and QR methods. However, for the F-19 chemical shifts in UF6-nClpi compounds, only some experimental trends could be reproduced by the calculations. Possible explanations are discussed, for these shortcomings, including the choice of model XC functional.