For modern tissue engineering, we need not only develop new hydrogels but also suitable processing methods for them. Polypeptides and polysaccharides are potential candidates because they can be methacrylated, processed before photocross-linking, and yielded into hydrogels with given shape and form. In this study, we successfully methacrylated collagen, gelatin, hyaluronan, and alginate to 30 and 60% degree of modification. We studied methacrylated compositions (i.e., precursors) to investigate their processability. The precursors of collagen and gelatin with 60% methacrylation exhibited suitable yield stress, shear-thinning properties, and fiber-forming capability for injecting and 3D bioprinting. On the contrary, the 30% methacrylated precursors had properties suitable for casting purposes. Our study also showed that the mechanical properties of hydrogels corresponded to the used photocross-linking conditions and the degree of modification. These results underline the importance of tunability of the precursors and resulting hydrogels according to the specific fabrication method and tissue engineering application.