The limitation of poor mechanical stability and difficulties in printing electrically conductive components can be overcome owing to the recent introduction of nanotechnology into the field of additive manufacturing (AM) and the consequent development of nonconventional polymer nanocomposites suitable for 3D printing. In the present work, different weight percentages (up to 6 wt % in total) of carbon-based nanostructures—multiwalled carbon nanotubes (MWCNTs), graphene nanoplatelets (GNPs), and a combination of both fillers (MWCNTs/GNPs)—were incorporated into poly(lactic) acid (PLA, Ingeo™) in an attempt to overcome several limitations of conventional 3D manufacturing based on insulating materials. Solution blending and melt mixing were the two fabrication methods adopted for preparation of the samples under test. A comparison of the morphological, rheological, and electrical properties of the resulting nanocomposites was carried out. Moreover, for the same weight concentrations, the influence of physical and geometrical features (i.e., functionalization and aspect ratio) of the embedded fillers was also investigated. Rheological methods were applied to control the quality of fillers dispersion in PLA matrix. The rheological percolation threshold was considered as reference in order to evaluate the internal structure of nanodispersions. TEM visualization, combined with rheological characterizations, was used for efficient control of the nanofiller dispersion. DC characterization revealed that lower electrical percolation thresholds and higher values of electrical conductivity were achieved using fillers with a larger aspect ratio and melt mixing, respectively. Moreover, given the possibility of obtaining complex and appropriate shapes for electromagnetic compatibility (EC) applications, electromagnetic (EM) response of the nanocomposites at the highest filler concentration was investigated in GHz and THz regions. It was found that the electromagnetic shielding efficiency (EMI) of nanocomposites strongly depended on the aspect ratio of the nanofillers, whereas the type of processing technique did not have a significant effect. Therefore, a careful choice of methods and materials must be made to address the final application for which these materials and further 3D printed architectures are designed.