The first series of Serial should definitely be your first listen, I binged on a lot of it while solo in Barcelona for 24 hours - I can remember special landmarks and exactly where I was in the series (and places I gasped out loud 😂).
If you become obsessed with the case, you could then go onto Undisclosed, which digs into loads more detail (but be aware it is biased towards one party because of the production team).
My Favorite Murder - this is my current go to podcast, but there are quite a few in jokes, so try to listen to some early ones to be in on it too.
Adam Buxton - lovely chats with people, some brilliant (I like it when he's with Joe Cornish and/or Louis Theroux, it all gets very funny and schoolboyish), some quite thoughtful.
Louis Theroux Grounded - expected output from Louis, but interesting conversations. I liked the recent Gail Porter one where she kept turning the interview back on him.
In a similar vein (vane?) to Serial, there's others like Dirty John, Dr Death, Teacher's Pet, Untold: the Daniel Morgan story, Paradise. All several episodes concerning one case. Have enjoyed all of these.
Stuff You Should Know is good if you fancy learning a bit about something while walking - we listen to this one with the kids.
There's so many, and really something for everyone.