See if you can find One Night in the Tropics. It was a real movie on its own before A&C were plugged into it. It starred Bob Cummings and Alan Jones, had two cute female leads and a couple of decent songs. The studio decided to try the boys out in film after their huge radio success. They were so good that they wrote and shot additional scenes after production and edited them in.
IMO, it is the only look we get at the "real" Abbott and Costello although Buck Privates comes close.
btw...for the best of Costello's pratfalls check out Who Done It? Chevy Chase dreams about being half as good as Lou in this one.