Kate is the oldest, and she should be married off before Bianca. Baptista wants to see both of his daughters well matched, but, even though he puts Bianca's suitor's officially on hold, he doesn't hold much hope for finding a good match for Kate. (Even when one comes he tries to tell him that he doesn't really want her). Does he care about his daughters' happiness? Sort of. He seems, however, befuddled by Kate. When an offer comes, he takes it, completely disregarding Kate's feelings on the matter.
He seems to care more about money than about his daughters' emotional well-being. An Elizabethan audience might be more sympathetic toward this position than a modern one. To us, he seems shrewd and calculating, especially when he gives Kate's hand away against her will.