Of course, the quote itself is probably apocryphal, but the sentiment still makes sense. It's easy to find information about military equipment, but what firearms were common in the civilian population of the United States during WWII?
This question is quite massive topic as in West Coast and Alaska there was little to none gun restriction (compared to modern-day world with exception of National Firearms Act of 1934 items and conceal carry regulations) and Americans use anything avalaible in ungodly numbers, even during Blair Mountain Battle coal miners were using black powder rifles from American Civil War.
But what was popular? Old mail-in gun catalogs show some light, like this 1927 Sears mail-in Catalog which show more or less shotguns (mostly side-by-side break-action shotguns), rimfire rifles and a small selection of centerfire hunting rifles (mostly lever-action). There was also catalogs offering pistols and revolvers (which latter were much more popular choice, USA stay with revolvers until 1980s, US made semi-auto pistols was rare sign prior to 1960s except rimfire pistols and .45 ACP 1911) and various milsurp (pretty much every gun once used by any army was at least once imported to USA in this era, there was multiple Lee-Enfields, various Gewehr models, P14/P17 rifles, unsold russian contracts including Mosin-Nagants made by Westinghouse and lever-action Winchester 1985 in russian standard-issue caliber) and imported guns (most popular were import small pistols from Europe in 6,35 mm Browning/25 ACP and 7,35 mm Browning/32 ACP and high grade hunting guns).
So, armed in 1930s. In rural areas you probably had a shotgun, rimfire rifle or old milsurp rifle, in urban and semi-urban areas more popular was revolvers in whole varietty of calibers. More afluent social groups may own lever-action or bolt-action hunting rifles or higher-end hunting shotguns. As a niche you can spot some semi-auto rifles produced by Winchester (Model 1905 and further models) and Remington (Remington Model 8). There was also pre-1934 private own machine pistols, machine guns, mortars, artillery, explosives etc. but in general in miniscule numbers.
But there is a catch, some states did have own sets of regulations eg. Michigan all pistols (defined as any firearm under 26 inches in overall length) must be licensed and person who want to have such gun had to apply for purcharce licence from State Police and register it, Southern States had whole sets of gun laws aimed at ethnic miniorities under Jim Crow law eg. North Carolina still require to obtain Pistol Purchase Permit from county Sheriff.