I am fairly new to shooting in general, and Cowboy Action Shooting in particular. If you’ve done it which SA pistol, lever action rifle and coach gun did you choose, and why?
Ruger Vaquero, Henry Big Boy, and an old Stevens hammered double cut at 19" long before my time.
If its the right match/crowd I substitute an early Colt SAA and a Winchester 1886. But then again I use a P-08 in military pistol shoots. 
Ruger Vaqueros, Winchester '94, Baikal 12ga.
What caliber pistol ammo did/do you use? Did you use the same ammo with your rifle? Why did you choose that caliber?
.45LC for the modern stuff and .44-40 in the antiques. I was on a serious .44-40 kick 35 years back and kept a fair number of them including a couple smoothbores I figure were made for indoor trap shooting. The modern stuff I worked up a load that performs well in both the pistol and rifle but I know a few of the hard-core serious people who keep separate supplies for each; muzzleloading I take WAY SERIOUS and the other stuff I do more as a fun-when-handy kind of thing. One of the top people around here is using .38/.357 for both because of how cheap and easy it is to get but there are some serious-tight-assed events that more look to earlier calibers. I would say check what is going on around you and take some of that as a lead. I am told that although there are standard practices the events in say Arizona are a bit different from what we have here in PA/Ohio.
PS – the Chinese-made coach guns seem to be popular such as the Century and others. And the prices on some through places like Dick’s are quite good. But again we’re talking coach guns; don’t rule out a strong older double and having it modified yourself.