You shouldn't send them in until you start your AMCAS application and print out one of their "Transcript Request" forms. This can be done in early May. Whether or not you want to enter Spring quarter grades is up to you. Most people, if they did at about the same level they did in previous quarters, will do so. Realistically, submitting on June 1 or June 15 is about the same thing, since most schools won't send out interview invites until early August anyway.