You might well find reading earlier ones to be a better place to start.
Whose Body is the first. Personally, I'm with Harry --
Gaudy Night is a favourite. But that's in large part because Harriet Vane is a favourite. She is introduced in
Strong Poison when Lord Peter prevents her hanging for murder.
For a standalone,
Murder Must Advertise is, as Harry suggests, one that works well without knowing any of the other characters or back story.