Aramid (AF), glass (GF), carbon (CF), basalt (BF), and flax (FF) fibers in the form of fabrics were used to produce the composites by hand-lay up method. The use of fabrics of similar grammage for composites’ manufacturing allowed for a comprehensive comparison of the properties of the final products. The most important task was to prepare a complex setup of mechanical and thermomechanical properties, supplemented by fire behavior analysis, and discuss both characteristics in their application range. The mechanical properties were investigated using tensile and flexural tests, as well as impact strength measurement. The investigation was improved by assessing thermomechanical properties under dynamic deformation conditions (dynamic mechanical–thermal analysis (DMTA)). All products were subjected to a fire test carried out using a cone calorimeter (CC).