Howdy again Cowboyjared!
If the authentic historical aspect of the 1870s-1880s (the Earp and Wild Bill era) interests you, I'd suggest looking more closely at that Cimmaron coach gun with it's external hammers; these would have been more common in the Old West of that era, than an internal hammered double like the Stoeger. Look at the 1866 and 1873 rifles and carbines also, as the 1892 Winchester, although good for a Hollywood western persona, would be too late for the earlier era.
As for handguns, cap and ball and conversions thereof would be correct for the era, but you could also go with 1873 Colt peacemakers and their clones (including the Ruger Vaquero). As you're new to cowboy action shooting, I'd stick with the 1873 peacemaker/clones. The Rugers will be easier to use and more reliable; one less thing to worry about when you're starting out. (I, too, went with Rugers initially, and still use them regularly even now for CAS.) As for calibers and powder, the authentic calibers to that era which are commonly available now are 45 colt and 44-40 for pistols and 44-40 for long guns. (There were no 45 colt long guns in the Old West.) The authentic powder would be black powder, not smokeless. As you're just starting out, and may have a limited budget, this is where I would break with historical tradition, and go with the historically later, but cheaper to shoot 38 special caliber in smokeless for both handguns and long guns. If you really enjoy CAS, at a future date, you could pick up some guns in more historically appropriate (and more expensive) calibers. Now if the mounted aspect really interests you, be aware, they only allow 45 colt in their pistols.
(For gunleather, check out the book "Packing Iron", which will give you tons of pictures of period correct gun leather from the mid 19th century to the early 20th century.)
Hope this helps!