Latin American colonial society was very hierarchical. A person's birth status did a great deal to determine what place in society he or she could possibly hold.
Of the groups you mention, mulattoes were at the bottom. These were people whose ancestry was part European and part African. These people were generally a bit lower than mestizos who were part European and part Indian. However, this could vary.
All mixed-blood groups were lower than the pure white groups. But even the whites were divided. The lower group was the creoles. These were people of European descent who were born in the colonies. They were seen as inferior to the peninsulares, who were Europeans who were born in Europe and came over to the colonies. The highest offices and statuses were reserved for the peninsulares. This was a major reason for the eventual creole-led rebellions that brought independence to Latin America.