One of our ol' hands was asked what someone needed to start in SASS.
The pards will loan you just about everything else. It's the Cowboy Way.
I've seen the damnedest mismatch of cowboy arms on the range. The shooter was safely having fun - and that's what counts. Most Cowfolk shoot a single caliber, just because of the easier logistics. However ideally, both pistols should be the same for consistent feel. Also, SASS shooters usually end up reloading with a progressive; and a single caliber makes things soooooo much easier.
The wifey and I shoot 38 Specials with a 125 gn FPTC lead boollet in front of Trailboss smokeless. Barely period correct, but definitely acceptable in the relaxed world of Cowboy Action Shooting. Roughly about half of the Cowboys shoot 38s; they make a lot of sense for recoil and economy. .45LC will earn you plenty of style points, and it makes the next largest percentage of shooters. The rest shoot a dogs breakfast of .32s, .357s, .44s, 38-40s, .44-40s, .32-20s, black powder, Russians, Schofields, etc., etc.... Your .44 Specials are fine, as long as you shoot lead and keep the fps down so you don't frag the posse and bend the targets.
To be competitive, you'll need ten in the leaver. A gun plumber can often shorten the magazine spring and follower to allow that tenth round.
Get yer donkey to the local SASS club, ASAP. Best things you can bring are ears, eyes and a smile.