Welcome Diesel40!
There are a LOT of different firearms available for Cowboy Action Shooting. Go to a shoot before you buy anything, and announce that you're new to the sport. I'd betcha that you find yourself trying out a bunch of different guns before the day is out. Each pistol feels different, and what works for me may not work for you.
When we started seven years ago, I bought two AWA pistols (Colt SAA clones), a Marlin 1894, and a Norinco external hammer side by side shotgun. After two matches, my wife had her set of AWAs, a Stoeger hammerless shotgun, and a Marlin Cowboy Competition rifle. We've since upgraded to the latest AWA Ultimate pistols (I like the AWAs because they need no action job; they're silky smooth out of the box). I've got a TTN external hammer shotgun, and she's got a Coyote Cap IAC '97 pump shotgun. We're both still shooting our first Marlins. I've still got all our first guns, and use them as backups and loaners.
All of these rifles and pistols are in .357/.38 special, primarily because of ammo cost. We shoot at least three or four matches a month, plus a number of annuals/majors. Even though I reload, the .38s are significantly cheaper.
We've got a number of additional guns now for CAS, including .45 caliber and percussion, but those above are our primary main match guns. They work for us. You'll find that many folks recommend the Ruger as your first pistol. They are excellent, rugged, and reliable revolvers. I just don't particularly like the way they feel. The Colt clone works best for us. The Stoeger is an excellent first shotgun, as far as side by sides go.
Again, the best bet is for you to go to a match and talk to folks. I guarantee that they'll just about force you to try out their guns. And you can decide for yourself what feels best!