As a teacher, I provide and encourage students to use the No Fear Shakespeare version of his works. The translations are so helpful! The books contain 1 page of Shakespearean text and 1 page of modern day text, so that if you stumble on the Shakespearean language, you can easily glance over to the modern day side to figure it out. No Fear Shakespeare is available at any bookstore for less than $7 and online for free.
Another good tip for studying Shakespeare is to do it with a group. Whether you’re reading for a class or for pleasure, it’s best to have someone else you can talk to and work through the language with. It makes it so much easier to double check your understanding when you have someone doing it with you!
Hope this helps you with the “language barrier”!