The Lord El-Melloi II Case Files series turned out to be a direct sequel to Fate/Zero that ends shortly before the beginning of Fate/Stay Night. Making it a perfect choice to watch between the two. Even better, it features two notable characters from Fate/Apocrypha and Prisma Illya (making it easier to watch those series afterward).
Content-wise it’s something like a detective mystery series infused with some standard Fate/-style action and occasional comic relief. The first episode is not representative of the series as a whole (the stand-alone episode 0 serves that role far better), to the point that if the backstory revealed within weren’t somewhat necessary I’d suggest skipping it entirely, while the rest of the episodes are split between an early episodic focus and a plot-driven remainder. There’s also a bit of a subfocus on philosophy, which would’ve probably ended up as boring as Zero‘s couch scenes had they not decided to keep the camera moving here. Even the most dialog-heavy sequences always have something to look at.
Maou-sama, Retry! unfortunately doesn’t compliment anything. It’s nothing but a pale imitation of Overlord with a worse protagonist and more gratuitous ecchi. Just ignore it.