The complexities of the ancient world are often lost on modern readers. The extended conversation in chapter six about fornication and "joining" with a prostitute seems, to the modern reader, to be a simple reminder to keep oneself sexually and morally pure. The complicating factor is that sexual intercourse was often a key factor in pagan temple worship. The primary goddess of the city of Corinth was "the goddess of love" and "ritual fornication" was an integral part of worship. The reference in 6:9 to "male prostitutes" is a reference to this same ritualized behavior. Paul's condemnation of this practice has as much to do with avoiding idolatry and returning to pagan worship than it does with more conventional sexual mores (although I believe, both apply).
The bottom line, sexual values aside, is glorifying God in body and spirit. How we live, how we steward our bodies, our time, our very selves does matter. Think of it this way. The human being is a unique blend of physical and spiritual being. Angels are pure spirit. Animals are pure physical. But human beings live life with a foot in both camps. We know that what impacts our bodies also impacts our spirit (try to pray when stricken with the flu). We also know that what impacts our spirit also impacts our bodies (that knot in the pit of our stomach when things are not right). The biblical goal is to seek and find balance. Balance between healthy physical living (faithful stewardship of our bodies) and healthy spiritual living (faith stewardship of our Spirit). The body and the spirit are not in competition with each other -- our physical self is not a burden nor is it inherently evil -- the harmony of body, mind, spirit and relationships is part of what the Kingdom of the Heavens is about. This is living life in "right relationship".
I didn't say much about the "lawsuit" issue in chapter 6. Suffice it to say that pride and the search for vengeance can cause us to do some pretty stupid things.