The recent development of fiber supercontinuum (SC) sources with ultra-low noise levels has been instrumental in advancing the state-of-the-art in a wide range of research topics. However, simultaneously satisfying the application demands of maximizing spectral bandwidth and minimizing noise is a major challenge that so far has been addressed with compromise, found by fine-tuning the characteristics of a single nonlinear fiber transforming the injected laser pulses into a broadband SC. In this work, we investigate a hybrid approach that splits the nonlinear dynamics into two discrete fibers optimized for nonlinear temporal compression and spectral broadening, respectively. This introduces new design degrees of freedom, making it possible to select the best fiber for each stage of the SC generation process. With experiments and simulations we study the benefits of this hybrid approach for three common and commercially available highly nonlinear fiber (HNLF) designs, focusing on flatness, bandwidth and relative intensity noise of the generated SC. In our results, hybrid all-normal dispersion (ANDi) HNLF stand out as they combine the broad spectral bandwidths associated with soliton dynamics with extremely low noise and smooth spectra known from normal dispersion nonlinearities. Hybrid ANDi HNLF are a simple and low-cost route for implementing ultra-low noise SC sources and scaling their repetition rate for various applications such as biophotonic imaging, coherent optical communications, or ultrafast photonics.