What types of business can a foreigner open with limited investment?

It depends on what you mean by limited investment.

But the surefire way we always recommend, is a business with the skills you already know.

The only thing you then have to worry about is learning the culture, setting up the business and getting customers. 

It's not a good idea to move to a different country and take on a business model that you are entirely unfamiliar with. That's a recipe for instant and painful disaster.