Never felt that Billy Martin had anything to do with the "Yankee Way", if there ever was such a thing. Bill James nailed him down pretty well when he speculated years ago on what Billy Martin would be doing if baseball didn't exist - 5 to 10 for manslaughter.
I'm a Yankee fan, but never bought into Reggie Jackson's hot dog antics and self aggrandizement. I remember the late Catfish Hunter saying something to the effect that Reggie was a great guy who'd give you the shirt off his back. And then hold a press conference the next day to tell everyone about it.
I do remember one Reggie moment that I treasure. In 1981, John Denny was pitching for Cleveland and knocked Reggie on his ass with an inside head high pitch. Reggie got up, hit a homer on the next pitch, and celebrated on his way around the bases. Denny went at him when he crossed home plate, and even though Denny was known as a strong guy, Reggie took him down and pinned him on the ground. They both were ejected, and I can still see Reggie laughing all the way to the dugout and clubhouse.