Saw this question on a different board, and thought it might make for good discussion.
Let's say for the sake of argument that an adult, out of school, decides to start reading Shakespeare. He asks, "What play should I start with?"
For the sake of discussion let's take "Don't read it, see it" off the table. Given real world constraints this is almost always going to mean, "Get the DVD" which turns this into an entirely different discussion about whose version of which play is acceptable.
Given a willing, educated adult who wishes to start reading Shakespeare plays, where should he start? Make your case.
Do you pick a tragedy, a comedy, a history? Do you go with Midsummer because it's supposedly so easy? Personally I don't think that one is easy at all to fully appreciate, I think that we teach it to young children entirely because of the fairy element and the silly Mechanicals. But that one's got some of the deepest poetry Shakespeare was capable of.
The best I could come up with for an answer went something like this:
There's a moment when children learn to read that they go from "I recognize those letters" to "that group of letters is a word" to "that group of words is a sentence," and so on. There comes a moment in understanding Shakespeare that you go from, "Shakespeare wrote the following words on the page" to "I understand why this character said these words because I know what he is feeling at that moment." The play changes when that happens. Once that happens, you'll never read the plays the same way again.
I realize that this doesn't answer the question, but I think that it's an important point to make. If you read the plays as nothing more than words on a page and never escape that feeling that you are "decoding" or "translating" what Shakespeare meant, you'll always be at a very shallow understanding of what you're reading. It won't really be understanding at all. It's like Shakespearean reading comprehension. Many children, when they learn to read, just go "word word word word word period word word word comma word word word..." in their heads, and nothing ever clicks to make them say, "Oh, ok! I get what's happening!" I think that a very similar thing happens for most people when they try to understand Shakespeare.
If I have to pick a play, I'm going to say Hamlet. I think that there are easier plays, but there's more that goes into the question than simply which one is easiest or shortest. Hamlet is "popular" (every other page you'll be spotting a modern cliche that came directly from the text). Hamlet is fairly easy to understand as far as plot goes. The character relationships (fathers and sons, men and women, brothers and sisters) are realistic. Most importantly, there's enough depth that you don't just read it once and check it off your list. You read it again and again and again and discover something new every time.