The Surface-enhanced Raman spectroscopy is the essential tool for various levels of the molecular studies. In order to become widely used as a fast analytical tool, the enhancing structures such as the nanoparticles have to be simple, inexpensive, and offer good flexibility in enhancing properties and the spectral range. In this paper, we investigated the plasmonic properties of the metal nanoparticles, to which the molecules of interest can be adsorbed, forming the bionanocomplexes. Here, for the first time, we provided the collection of the results gathered in one article, which can serve as the basis or guidance for designing the SERS studies on different bionanocomplexes, various nanoparticle structures, sizes, and excitation wavelengths. The presented plasmonic properties describe the spectral position of the plasmonic resonances as results of their size and structure. The electric field enhancement as a key contributor to the SERS effect is given as well. We considered silver and gold nanoparticles and their variations. Gold is one of the best choice, due to its relevant surface properties, however, suffers from the plasmonic activity and rather static spectral position of the plasmonic resonances. Therefore, one of the main purposes was to show the effective resonance tuning using simple and less expensive geometries. We showed the possibility to adjust the plasmonic resonances with the excitation wavelengths from the blue region to the near infrared region of lasers most commonly used for Raman spectroscopy. The presented studies indicated the high potential of the core-shell structures for this kind of applications.