People usually mean low-skilled immigrants when they talk about economic migration. High-skilled immigrants are more likely to choose a particular company or even a specific job opportunity than a specific country. They don't move to a country because they want to live there but because many of the best opportunities for a person with their particular skills and networks happen to be there. They don't choose between country A and country B when they don't have any particular reason to move, but between taking a specific opportunity in country A and not taking the opportunity.

It really depends on where the immigrant in question is coming from. I definitely shopped for countries back in the day.