Soul Calibur is often very strong with solo content. SCV being an exception and I haven't played VI yet. I hear it's ok with solo content, but not as strong as the old games.
NRS games like MK and Injustice are fine. I'm not a fan of the actual fighting engine, but the content is good. Injustice have solid campaigns(comic prequel books are way better and highly recommended reads too!).
ARC games like Blazblue have some very, very lengthy narratives. Visual Novels really with some occasional fights and choices to make. It's ridiculous and very anime, but the content is typically absurd and you get to know the fighters lore and backgrounds real well. I actually really dig that as it feels like the universe is fleshed out, but the actual fighting is complicated and becomes a crutch if you don't care to really learn it.
DOA5 had a cute story mode. Longer than most but not super memorable. Tons of costumes to unlock(even without dlc) made playing its other modes a bit worthwhile. I find the fighting real fun. Not too complex and very approachable. Very flashy too.