We investigate Magnetic Josephson Junction (MJJ) - a superconducting device with ferromagnetic barrier for a scalable high-density cryogenic memory compatible with energy-efficient single flux quantum (SFQ) circuits. The superconductor-insulator-superconductor-ferromagnet-superconductor (SISFS) MJJs are analyzed both experimentally and theoretically. We found that the properties of SISFS junctions fall into two distinct classes based on the thickness of S layer. We fabricate Nb-Al/AlOx-Nb-PdFe-Nb SISFS MJJs using a co-processing approach with a combination of HYPRES and ISSP fabrication processes. The resultant SISFS structure with thin superconducting S-layer is substantially affected by the ferromagnetic layer as a whole. We fabricate these type of junctions to reach the device compatibility with conventional SIS junctions used for superconducting SFQ electronics to ensure a seamless integration of MJJ-based circuits and SIS JJ-based ultra-fast digital SFQ circuits. We report experimental results for MJJs, demonstrating their applicability for superconducting memory and digital circuits. These MJJs exhibit IcRn product only ~30% lower than that of conventional SIS junctions co-produced in the same fabrication. Analytical calculations for these SISFS structures are in a good agreement with the experiment. We discuss application of MJJ devices for memory and programmable logic circuits.