A&C was the second Shakespeare play I read, back in the ninth grade. Still one of my favorites. It's also, technically, a sequel, since Antony's a major character in Julius Caesar before this.

There's actually a lot of debate about the chronology of his plays, because not every performance was recorded (we know Romeo and Juliet was performed in his lifetime, but there's no record of a specific performance until after his death), and plays were published after they were performed, often years later.

That said, the chronology most often cited suggests that he did write a bunch of them back-to-back, but when they were performed is more uncertain.