First, find a club and try the game out with someone else's guns. Borrowing guns at a club match is seldom a problem.
for a BUNCH of information.
Generally, the guns required are two single action revolvers, either cartridge or percussion, a lever action rifle in a "pistol caliber" (we call 'em pistols for some reason), and a SxS shotgun, 1897 pump, or even a single shot in 20g, 16g, 12g, or 10g.
That said, there are pump rifles made for the game, but they usually are problematic. There is also the 1887 lever action shotgun. Rifle & pistol calibers can be most any traditional cartridge from .32 H&R magnum up to .45 Colt. Some categories have caliber restrictions, some require certain guns, such as fixed sight instead of adjustable sight, and some have specific costuming requirements. Calibers include .32 H&R magnum, .38 spl, .357 mag, .38-40, .41 mag, .44-40, .44 Russian, .44 spl, .44 mag, and .45 Colt. Single actions chambered in 9mm, .40 S&W, and .45acp are also legal in some categories. Percussion guns from .36 to .44/.45 are also legal.
There are some rifle calibers, such as .32-20 and .56-.50 that are also legal, and a rifle/pistol cartridge called the Cowboy .45 Special.
I've probably missed a couple in there somewhere, but you get the idea.
Check out the shooters manual HERE