If you want to get into some neo-big band, you could check out Big Bad Voodoo Daddy.
My suggested album would be their
Americana Deluxe from 1998.
edit :
Squirrel Nut Zippers may not fit the big band description perfectly, but they do retro swing jazz and other genres and are very good I think.
Suggested album would be
Perennial Favorites, also from 1998!