I would start thinking about your essays as soon as possible. Obviously, you will want to focus on your GMAT first, and get a solid score out of the way...but then I would move on to brainstorming and content development phase of the application essays. When time is on your side, and you can spend months crafting your story, refining your leads, and editing transitions, you will be much less stressed and, therefore, have much more fun. That said, June is a sufficient amount of time, even for Round 1, but the pressure will start mounting quickly, especially if you have essays to complete for 6-8 schools.
Essay content development and editing is my favorite part of the process, when working with clients, so let me know if you have any other questions or concerns. I wish you all the best.
