Stephen Sondheim and Jule Styne wrote the song for the 1959 musical Gypsy. (Here's the number from the film.) It was arranged by Billy May and recorded in 1967. Amazon track is here.
Belated edit: Mark Steyn adds:
As for "All I Need Is The Girl", that's a great Billy May arrangement of a Jule Styne/Stephen Sondheim number from Gypsy. Jule Styne told me he'd always wanted to write for Fred Astaire, but the opportunity had never arisen. So in 1959 he decided to write a Fred Astaire number for the young kid to do in Gypsy. At the first-night party, Astaire walked up to Jule and sang, "Got my tweed pressed, got my best vest..."