Jerry Mathers said that he and Tony Dow were very lucky during their acting careers: when they got the chance to make "Leave It To Beaver", serendipity chose good people for the roles of Ward and June. Hugh Beaumont was a Methodist Minister, but also a thoughtful, intelligent man. Barbara Billingsley had two kids of her own, basically the same age as Wally and The Beav. Both treated the kids as if they were there own and it showed.
Though Hugh hadn't been cast in the Pilot, he auditioned with Jerry, who prayed that Hugh would get the role. He had worked with Hugh in a religious tome and liked him a lot.
My parents had a really nasty divorce and I, like Jerry and Wally, leaned on Hugh/Ward as a substitute when my Dad wasn't available.