As part of the present work, polymer composites used in 3D printing technology, especially in Melted and Extruded Manufacturing (MEM) technology, were obtained. The influence of modified fillers such as alumina modified silica, quaternary ammonium bentonite, lignin/silicon dioxide hybrid filler and unmodified multiwalled carbon nanotubes on the properties of polycarbonate (PC) composites was investigated. In the first part of the work, the polymer and its composites containing 0.5–3 wt.% filler were used to obtain a filament using the proprietary technological line. The moldings for testing functional properties were obtained with the use of 3D printing and injection molding techniques. In the next part of the work, the rheological properties—mass flow rate (MFR) and mechanical properties—Rockwell hardness, Charpy impact strength and static tensile strength with Young’s modulus were examined. The structure of the obtained composites was also described and determined using scanning electron microscopy (SEM). The porosity, roughness and dimensional stability of samples obtained by 3D printing were also determined. On the other hand, the physicochemical properties were presented on the basis of the research results using thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), wide angle X-ray scattering analysis (WAXS) and Fourier Transform infrared spectroscopy (FT-IR). Additionally, the electrical conductivity of the obtained composites was investigated. On the basis of the obtained results, it was found that both the amount and the type of filler significantly affected the functional properties of the composites tested in the study.