Read Hamlet, Macbeth or Othello. King Lear and Antony and Cleopatra are the other major tragedies, but Lear I think is pretty hard going at times and A&C I personally don't enjoy as much as any of the other three (I'm sure others will disagree).
Read a version with some easy to refer to notes to help with the archaic words. But don't get too attached to the notes. Ideally, either watch the play or listen to the play before you read it, because there's a danger in getting bogged down in the language and not recognising that these were written to entertain everyone from royalty to plebs. Also hearing how the lines are "supposed" to be read is important because (as a rule) we don't know how to read poetry aloud in this day and age.