Andy Williams and Perry Como were great on TV. Perry Como singing "Ave Maria"! Both men had a warmth that played so well on the small screen. Interesting that at this time it tends to be the "cool" personas who do well on TV, or the visibly highly neurotic!
Speaking of neurotic, I've seen snippets of Judy Garland's TV show on youtube and much of it was fantastic, depite the difficulty they seem to have had putting it on the air. And if you google something like "Judy Garland's Christmas Special" it's great fun to watch. It has teenage Liza and younger children Lorna and Joey, all of whom perform with their mother. Judy was just an incredible, electric, mesmerizing talent.
I think you can also google whole chunks of Frank Sinatra specials too. What a great era of television!