I picked up Conan the Barbarian on the cheap* at Barnes & Noble some time last year as a Christmas gift to my brother-in-law, who likes fantasy and sci-fi. Later on, I couldn't resist picking up a copy for myself. I'd never read any of the Conan stories, nor seen any of the movies. However, it seemed that if they were still being published, they might be worth the read. They are, by the way.
Here's the edition I picked up, published by Metro Books.
There were nine short stories/novellas, and I began to think that perhaps looking into full-length Conan novels by Robert Howard--the original author--would be a worthwhile idea. I consulted Wikipedia (please spare me your judgment) and discovered that the cover blurbs had been a bit misleading. (If you've not yet read the footnote, now would be a good time.) The collection I had purchased only contained some of Howard's Conan tales--the last nine, I believe.
Anyway, if you found yourself in the same predicament, my suggestion is to pick up this one: The Coming of Conan the Cimmerian. (Del Rey)
True, there is some overlap (two, maybe three stories,) but it contains the earlier stories you missed--and gives the orginal titles and "Weird Tales" publication dates.
*Well, just under $10, anyway, which seemed like a great deal for "The original, unabridged adventures" of "the original Conan epics."