I know that plays by Shakespeare might look especially daunting to read, but even if the language is a bit more outdated and difficult to understand, it is still more than well worth it to immerse yourself in Shakespearean literature. The different plays teach you different lessons, highlight different principles, and point out different human outlooks, opinions, and ideas.
Now, the first play you might think of by Shakespeare is Romeo and Juliet, because that is what the majority of school systems emphasize and have children read. However, even though that play introduced the idea of forbidden love, I find the whole thing utterly depressing, because I believe that the negative of so many deaths outweighs the positive of a new kind of plot.
So instead, I think that the first play of Shakespeare you should start with is The Tempest. It centers around a man named Prospero who used to be the duke of Milan. However, his brother took the throne from him and drove him and his daughter out so that by the time the play opens, they are on a deserted island. But then his brother and the others who helped him overthrow Prospero get shipwrecked on the same island, all thanks to Prospero having one of his magical friends control the winds. He is now free to exact his revenge, stop more evil from coming to pass, and make sure happiness comes in the future, all in the way he decides his actions in a few days. I highly recommend it.