School is generally thought to be a fast-track to experience. That is, a degree translates to N years of experience in the real world. In reality (at least according to my experience), the MBA degree is merely a ticket to an interview. If you got your MBA in Management and Project Innovation, you might have a leg up on non-MBA holders, but you'll still wind up with a bit of trial-by-fire, since you don't have a lot of real world experience. Plus, grad school can be expensive.

Another route would be to go straight into the workforce and do some real-world software engineering. You'll find out really fast whether the coding-to-decision ratio is good enough for you, or whether you really want to move up into management. As others will tell you, management is a whole different animal. For most technically minded people like software engineers, they usually only want to make technical decisions. Managers, on the other hand, have to think about a lot more, especially on the business and people side of things.

Find a mentor and learn as much as you can. At first, this should merely be a lead engineer. They'll have experience making decisions AND the technical chops to back it up. If you reach the position of Lead Engineer and you still want to get into management, find another mentor. (Hint: mentors are a fantastic way to move up in organizations and learn a lot in the process).

And above all, don't rush into anything. You have your whole career ahead of you. Enjoy it as much as you can.

Good luck.