The first song I ever learned to play was actually two old folk songs: Deep Blue Sea and Oh Mary, Don't you Weep. The first cool song I learned was Mr. Tambourine Man. I was 11 or 12 in summer camp. A counselor taught the song to me and one of my bunk mates. The two of us stayed up to the wee hours of the morning playing it over and over and over again.
As for bad Dead tunes, IMHO, Money, Money, France, and Antwerp's Placebo can give Let Me Sing Your Blues Away some serious competition.
Bill, tgo