Where to start? First thing is- the Bard of Avon wrote comedies, tragedies and histories. Out of these 3 categories I recommend:
1. Comedy - close call between A Midsummer Night's Dream and Much Ado About Nothing (or as we say in Yorkshire Much Fuss Over Nowt!)
2. Tragedy - MacBeth (The Scottish Play) or Hamlet.
3. History - Henry IV or Richard III.
It is best to read a little before seeing a Shakespeare play for the first time - there are many modern books that summarise the plays and books that have created stories out of the plays. Start simple and build up. Or watch a t.v version or dvd then go see the play live because that's where true magic lies.
May your appetite be whetted. Then come over to Stratford and see the RSC at work.