Round 1 deadlines are typically around early October, and round 2 deadlines would be somewhere in January. Round 3 should only be considered as a last resort, as schools usually fill most of their slots with applicants from the first two rounds.
The score from your GMAT will be sent to you and all of the schools you indicated within 20 days of your test. This means that if possible, you should try to knock the GMAT out by early September, giving your score report enough time to reach your selected schools before the October deadline, assuming that you really want to make the Round 1 deadline.
Hi, I'm DonQuixote, a former GMAT Pill student who scored 780. I'm very grateful for this score and have now joined their staff My account of my GMAT experience can be found here.