What kind of family is the Clutter household? In what way does Capote create sympathy for them?

You have a large (four children) hard working, honest farm family. THey made their money through hard work and built up a successful far. This is what America loves. Honesty, love, hard work and a farm is as close to the American definition of prefect that you can get. I think that is where the sympathy comes for this family when things go so wrong.