With regards to whether you should apply to Round 1 or 2, you should apply when you feel your application is most ready. There is no clear advantage to applying to a particular round. The only exception is to avoid applying to the last round, as the acceptance rates are notoriously lower.
With regards to other programs you are interested in, do you have a location preference in the US? There is a large advantage to attending an MBA program in the location where you would like to work post-graduation.
Even more than the years of work experience that you have, business schools want to see increased responsibility and leadership experience in your career.
I hope this was of help.
Conrad and the Stacy Blackman
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MBA blogger, US News and Author, The MBA Application Roadmap