Which branch should I join?

I wouldn't worry too much about promotions. If you can fog a mirror, you'll make Captain at the same time as everybody else in your year group. Keep your nose clean and do what you're supposed to and Major is almost assured, just a question of whether you make it above or below the zone (late or early) or at the same time as everyone else.

Lt Col gets you to 20 and I don't think that's all that hard either. You said you're planning to get your MBA. That's one of the squares you have to fill. There are a few other training requirements. Complete them and stay out of trouble and you'll make Lt Col.

Full bird Colonel is another story. You have to be hand picked and really be on your game for that one. But not required to retire with 20 years.