Those dates actually a bit off, the 40's and 50's were when pulp was mostly winding down, the 20's and 30's were the height of pulp but it began way back in 1896. As far as where to start, well that depends entirely on what kind of fiction you're interested in, the pulps were made in every genre. If you just want a sampling then pulpgen.com has over a thousand stories, most of them short, divided up by magazine, everything from hard-boiled detectives, to damsel saving adventurers, to sappy romances.
If you like crime fiction then I recommend Dashiell Hammett and Raymond Chandler. If you like adventure then I recommend just about anything by Edgar Rice Burroughs especially the Tarzan and John Carter of Mars novels, also you can never go wrong with Doc Savage.
If you want to purchase actual books there's been a huge increase in interest, and therefore publication, of pulp reprints lately. There have been two big omnibuses of crime fiction The Big Book of Pulps and The Big Book of Black Mask, the latter of which collects stories from Black Mask Magazine, the magazine that inspired the movie the most. Sanctum press sells the Conde Nast heroes (Doc Savage, The Shadow, and The Avenger basically the big names). Atlus Press publishes omnibuses containing the lesser known heroes (Ki-Gor, The Black Bat, Secret Agent X etc.) in complete volumes in publication order. Girasol Collectables reprints The Spider and does replicas of pulp mags ads and all, pricy but very nice. Radio Archives does ebooks of The Spider, Operator #5 and a few others. Finally Adventure House has High Adventure a bimonthly publication that usually spotlights a single character, either a whole novel, or a handful of shorter stories, they also do replicas of various pulps.
EDIT: Apologies for the incredibly disjointed and poorly put together post, I kept adding on and rearranging it, resulting in the mess you see before you.