The Three-Fifths Clause and Representation in the House of Representatives

Article I, Section 2 of the original Constitution provided: 

"Representatives and direct taxes shall be apportioned among the several states which may be included within this union, according to their respective numbers, which shall be determined by adding to the whole number of free persons, including those bound to service for a term of years, and excluding Indians not taxed, three fifths of all other Persons."

 Did the Southern States demand a Three-Fifths Clause? Or would they have been happy with representation in the House being apportioned "according to their respective numbers of all persons"?

What fraction would have pleased the South? Zero-Fifths? Three-Fifths? Five-Fifths? 

What fraction would have pleased the North? Zero-Fifths? Three-Fifths? Five-Fifths? 

Is the real problem proportional representation in the House (as opposed to each state being allocated, for example, 10 seats in the House without regard to population)? Or is the problem that slavery existed in the Southern states resulting in some human persons in slave states being denied fundamental freedoms?

Discuss.