If you apply Round 1 and receive an admit, you mostly likely will have to pay your deposit prior to round 2 decisions from other schools. Most top schools will begin posting their application deadlines and decision deadlines in June. Many schools will also post their deposit deadlines for each round, so this is something you can begin to plan for soon.
In terms of timeline for essays and planning applications, you should allow much more time than you think you'll need for application essays. Personally, I began writing my essays last August while studying for the GMAT. I took the GMAT September 3rd and then began focusing seriously on essays, but soon realized I would not be ready even for late October application deadlines. I worked right up until the Round 2 deadlines for almost all of my schools.
In terms of when to apply to your dream school, I think it depends on how much risk you are willing to assume. A more conservative approach would be to postpone applying to your top choice until Round 2, so that you could use any Round 1 admits/dings to gauge your competitiveness at your top choice. However, if you feel confident enough in your application package prior to the Round 1 deadline, then you should definitely apply round one. At most schools Round One will give you a better shot at scholarships and grants, and having a few extra months to plan your move to grad school is always nice.
One more thing- don't underestimate the time and work it will take to prep your recommenders. If the people writing your recommendations have not done a recommendation letter for a top business school before, you will need to give them a lot of information to assist them with the process.