Standards I'd love to see Jerry do a lesson on:

His renditions of  "Stormy Weather" and "Lullaby of Birdland" 

A Glenn Miller #, maybe "Tuxedo Junction" because it's so bluesy.

Something by Hoagy Carmichael ("Buttermilk Sky"?)

"Your Cheating Heart" or some other Hank Williams.

One of the Nat King Cole Latin boleros such as "Perfidia"