I initially wanted to apply in June or July but I kept on getting hung up on the personal statement and other application stuff like letter of rec. I would suggest for you to ask for letter of rec now, and start writing your personal statement. By the time May comes around, you will only have a few things to finish and summit in June and be within the first hundred. But if you have excellent stats, then you will have more time to procrastinate.
Don't even think about applying on the lastest dates. No reason for that, and every school has different deadlines. Most are around Jan to Feb or even March, but at that time, you have to be a superstar to get excepted.