Dilemma: to what schools to apply first?

The differences among rounds is a bit overblown, if you ask me.

I would just try to come up with a schedule that allows you to include some schools from each category in each round, without getting burned out. Part of this will have to do as much with the schools' individual deadlines within a round as anything else.

I would do maybe something like this:
Rd 1: Euro School 1, Yale, HBS, Columbia (in that order)
Rd 2: Booth , Kellogg, Duke, Euro School 2 (in that order)
Rd 3 (optional): Euro Schools 3 & 4

My reasoning is that--no matter how confident you are in your abilities--your application will evolve and your process will get much tighter as you progress through the first round. For that reason, you don't want to begin with your dream school. Rather, it's best to develop your application using a "backup" school. For round two, the effect is less pronounced, and I'd rather just attack my top choice immediately.

This is, of course, subject to your personal school preferences, and actual deadlines.

Also, don't dilute your candidacy by applying to too many schools. If you know deep down that you'd rather wait a year and reapply than to go to a program, you might as well save the time and money.

Finally, plans fall through. I didn't get to apply to a lot of my top schools because I simply got sick of spending all of my free time on applications. I was lucky to get into a couple of amazing programs, but I still wonder whether I would have gotten into some of my other targets.