blimp:
Start with Lear, then read Othello
I agree - almost. But I would say not 'read' but 'watch'. Shakespeare didn't write closet drama; his plays are meant to be seen, and a good production brings it all to life, and makes the sometimes difficult language clear.
There is a glorious film version of Othello with Kenneth Branagh as the evil Iago. Personally, I would go for Julius Caesar first, because in Cassius one can see a precursor of Iago, in the way he manipulates the noble Brutus.
In my opinion there is no finer speech in English literature than Antony's funeral oration - 'I am no orator, as Brutus is; But, as you know me all, a plain blunt man' - my bum!
