I would particularly recommend Hamlet, Macbeth, King Lear, The Tempest, Othello and Romeo and Juliet as the plays of his that have probably been most influential on drama (not just Western drama either) and the English language. It is wild how much of what we say and how we say it basically originates with Shakespeare. Even just seeing 2-3 of them can make a real difference to one's understanding of drama I think. Really helps to see them on stage performed well I think, but that's not something everyone has easy access to. I say this particularly because Hamlet can go very easily from fascinating to kind of dull depending on the quality of performance. Macbeth is rather more robust - it's a lot harder to screw up and rather designed for scenery-chewing (I saw a really fun performance of it at The Globe last year, with the witches as three men in crime scene tech outfits - sometimes with gas masks - and Estuary accents, which worked bizarrely well!). A lot of the movie versions are, like, at least acceptable. Better than nothing! Romeo + Juliet was certainly more compelling than any stage take of the same I've seen.