Deadlines for the 2011/12 season were as follows:
Round 1: October 3, 2011
Round 2: January 4, 2012
Round 3: March 5, 2012
Deadlines for 2012/13 haven't been set yet, but are likely to be similar. You can expect the new deadlines and essay topics to be published in June/July, with the online application system itself going live in July/August.
Your admission chances are the same in either R1 or R2, but your chances are of course stronger if you take the time to prepare a quality application, rather than rushing to submit at the earliest opportunity. If waiting allows you to submit a stronger application, then that is what you should do.
R3 numbers vary from year to year, but potentially can be much tighter, and it is generally recommended that international students avoid applying in R3 (due to the time taken to process student visas).
There is no advantage to applying early within a round - adcom won't start reviewing applications until after the deadline anyway.