Ready-to-run American cars suitable for 1930-1949 era:
Athearn: 1931 Ford Model A, pickup, sedan and sport coupe (great model with lots of colors, buy lots).
Busch: 1931 Ford Model AA panel truck, 1947-49 Dodge Power Wagon, 1950 Buick Special Riviera Hardtop (introduced Fall 1949).
Classic Metal Works: 1936 Ford, 1941 Plymouth Coupe, 1948 Ford Convertible.
Masterpiece: 1934 Chrysler Airflow Imperial Eight (New model that should be available either at the end of August or beginning of September).
Ricko: 1931 Lincoln Model A (available with top up or down), 1934 Cadillac Aerodynamic Coupe.
Roco: Willys Jeep, CCKW 2.5-ton truck.
Woodland Scenics: "Auto Scenes" 1939 Ford.
Not American, but look right for the period:
Brekina: 1934 Citroen Traction Avant (A company in Los Angeles sold them as the Challenger in the United States).
Busch: 1931-35 Mercedes 170V sedan, Busch 1935 Horch 835 Cabriolet, Busch 1937 BMW 327, 1945 MG TC roadster.
Ricko: 1927 Mercedes-Benz 630K Cabriolet (available with top up or down), 1935 Horch 851 Pullman, 1936 Wanderer W25 Roadster, 1939 Horch 930 Convertible (available with top up or down).
In addition, there are some excellent kits available from Jordan Highway Miniatures, Greg's Garage, Sylvan Scale Models (highly recommended) and others.
If you can find some of the discontinued Wikings, like the Horch 850 and Mercedes-Benz 540K, they are often fairly cheap and look right at home. Wiking also had some old Mercedes trucks, the L2500 moving van looks good.
This isn't an exhaustive list; just what I could remember off the top of my head.
By the way, the CMW large trucks are not suitable. Despite what has been said, the White WC-22 actually was produced from 1950 to 1959. The White COE is a 1953 model and the IH-R190 dates from 1954. The bus is also from the early 1950s.
Sorry, none of the Wal-Mart cheapies are correct.