I have the book Anarchy and the Law (edited by Stringham) which has an excerpt from Friedman’s book. It is indeed an excellent excerpt, so the book is probably good as a whole too. Friedman does take the argument from a utilitarian perspective, but so does Rothbard, to an extent. Rothbard often shows how a libertarian society would leave everyone better off and then he includes why it would be morally superior from his natural rights POV.
Also, I have no clue why you mentioned the Chicago School. David Friedman is an Austrian just like Rothbard. I think you might have mixed him up with Milton Friedman, who was the famous monetarist and leader of the Chicago School in the 20th century who brought semi-libertarian economics to the forefront.
Hold your horses - an Austrian!? I think he works within the neoclassical framework. He might have some affinities with Austrianism, but none that I’ve noticed really, aside from support for anarchism. Anyway, his book is great. I prefer Rothbard’s FANL and Hoppe’s DTGTF, but his book is also a great primer, and is good for converting the “average Joe” type.