I have also included some other stuff that has resulted from my research, with notes about each track below.
If I Had A Million Dollars - The Boswell Sisters - classic tune, classic interpretation.
Oh Johnny, Oh Johnny, Oh! - The Andrews Sisters - lovelovelovelovelovelove
Don't Sit Under The Apple Tree - The Andrews Sisters - i think their most popular tune ever
42nd Street - Boswell Sisters - For any musical theatre freaks: interesting. listen to this.
I had to include ballads as well:
I'll Be With You In Apple Blossom Time - The Andrews Sisters - pretty. something about an 'apple' theme here though
I Love You As I've Never Loved Before - The Mills Brothers Their only barbershop stuff i can find. but listen to the first minute and a half at least and follow the bass voice allllllllll the way down to the low C (or whatever). Ridiculous.