He wrote both comedies and tradegies, as well as histories.

He used a lot of plays on words. In particular, he was really great at using irony (think Marc Antony's speech at Caesar's funeral).

(Ask a historian, but I think his history is a little suspect.)

Just in general: here we have one of the most famous people who ever lived - in fact, whose fame has easily transcended "western culture" - and there are still a lot of things about him that are not known with certainty.

He liked to use the soliloquy. He may have acquired this technique, as he acquired much of the inspiration for his stories, from his familiarity with greek and latin.

He wrote over 150 sonnets.
Sonnets have 14 lines and most of the sonnets use iambic pentameter.
The rhyme scheme for a sonnet is abab cdcd efef gg.

Worth memorizing:
Sonnet XXIX

First part of ANTONY's speech in JC, Act III
"Friends, Romans, countrymen, lend me your ears;
I come to bury Caesar, not to praise him.
The evil that men do lives after them;
The good is oft interred with their bones;
So let it be with Caesar."

Last part of Polonius' advice to Laertes
(bearing in mind that this, too, is irony -
because of Polonius' character)
"This above all: to thine own self be true,
And it must follow, as the night the day,
Thou canst not then be false to any man."

First part of the balcony scene in Romeo and Juliet
"But, soft! What light through yonder window breaks?
It is the east, and Juliet is the sun."

From Hamlet's soliloquy
"To be, or not to be, that is the question:
Whether 'tis nobler in the mind to suffer
The slings and arrows of outrageous fortune,
Or to take arms against a sea of troubles,
And by opposing, end them."

To get the effect of these, one might give a synopsis of the story or of the character involved, recite the entire passage and discuss it's meaning and import, and then commit these very few parts to memory.

I don't know how much time you will spend on this unit, but hopefully you will have sufficient time to go through at least one play in its entirety. (I've always been partial to JC.)