With some series, it almost doesn’t matter where you pick up. Oh, sure, there’s a larger story arc across the series, but each book or story is written such that it can stand alone. Everything you need to understand what’s going on in the story is present in that story.
Jim Butcher does a good job of this with the Dresden Files. Yes, there’s a larger arc in Harry’s life through the series, but each book describes his home, tells about his basement laboratory and his “assistant” Bob, and gives a brief description of any relevant character and how and why Harry knows them. (Okay, I was a little confused when Michael Carpenter first showed up, but generally speaking, especially with recurring characters, they’re handled well.)
Some people don’t do this as well. In another series (that will remain nameless), I picked up the fifth book because it was the only one my library had. In the first chapter, the main character said about someone else that she didn’t understand why the other character was behaving in a given fashion, that the action made no sense to her, and that she went along with it. I put the book down and never read anything else by this author because I figured either the main character was too stupid to live and shouldn’t have gotten to the fifth book OR the author was assuming that readers, based on previous experience with the main and secondary characters, would agree that was a sensible method to behave. I didn’t have that experience.
Anything we write may be the first story (or blog post) that a reader finds of ours. If it doesn’t make sense or provide us with the tools to make it make sense, it fails for that reader.
This was recently brought home to me in a rejection of a short story. The editor said that it felt like part of a larger whole, a series where the reader might not know all that was going on with the characters. I had conceived the MCs as series characters (although, failing so far to sell this story, I haven’t written any more) and wrote a story where only a partial character arc was shown, without explaining any of the emotions or history behind it for the two main characters.
That might work for a chapter in a book, but it doesn’t for a short story.
Now I know what I’ve got to change with edits. Maybe that will translate into an acceptance the next time the story goes out. First, however, I have to do the work.