The need of the synthesis of a new generation of medicines aimed at combating bacteria and biofilms that cause various infections is a great urgency. There has been a gradual decrease in the conventional techniques of treatment with the use of antibiotics. Consequently, much effort has focused on the search for new methods and approaches to obtain antibacterial drugs and determine their rational use such that microorganisms do not acquire resistance. Although silver nanoparticles (AgNPs) and silver nanoclusters (AgNCs) have exhibited certain levels of effectiveness against multidrug-resistant bacteria and biofilms, there are very few simple, cheap and easy-to-scale methods to obtain AgNPs and AgNCs with well-desired characteristics. In this study, we carried out the one-pot synthesis of sols and gels containing AgNPs and AgNCs using only L-cysteine (CYS) or N-acetyl-L-cysteine (NAC), as bioreducing/capping/gel-forming agents, and different silver salts – nitrate, nitrite and acetate. HRTEM, SAED, EDX mapping, AFM, SEM, EDX, ICP-MS and FTIR spectroscopy analysis confirmed the formation of spherical/elliptical CYS-AgNP and NAC-AgNC particles consisting of AgNPs or AgNCs “core” and CYS/Ag+ or NAC/Ag+ complexes “shell” with mean average diameters of 10 and 5 nm, respectively. UV-Vis spectroscopy fixed the localized surface plasmon resonance (LSPR) at 390–420 nm for the CYS-AgNPs systems and LSPR absence for the NAC-AgNCs ones. DLS and nanoparticle tracking analysis (NTA) data indicated that the mean average diameter of the particles is about 80 nm for the CYS-AgNPs systems and 20 nm for the NAC-AgNCs ones. The Zeta potential measurements showed that the particles possess positive and negative charge values for CYS-AgNPs and NAC-AgNCs systems, respectively. The prepared materials demonstrated the high antibacterial activity against the most common types of bacteria at the MIC range of 10–100 μM, wherein the effect of the NAC-AgNCs systems is 2 times stronger than that of the CYS-AgNPs ones. Both systems are non-toxic or have low-toxicity at 300 μM for normal human cells: erytrocytes, fibroblasts and macrophages. Sols and hydrogels in the concentration range of 20–40 μM showed the complete inhibition of the formation of biofilms from Acinetobacter baumannii and Pseudomonas aeruginosa, which belong to the ESKAPE pathogenes group and represent the most serious problem in practical medicine. NAC-AgNCs systems were the most active. The simple strategy of the preparation of AgNP/AgNC-based sols and gels, along with their pronounced antibacterial and antibiofilm activity, could open new perspectives for its applications in medicine.