OK, let's try this again.
It sounds like you are getting some misinformation. Let's work backwards. The only category that allows you to have 2 loaded pistols in your hands at once is gunfighter. Generally speaking, in gunfighter, you alternate your shots on the targets between your pistols. Shoot one pistol, then the other, then the first one again, then the second one again, etc.
You really need to get to a match and watch how this stuff is done, and I suggest you do so for before you spend one red cent, so you don't spend money on what might be a misunderstanding of the rules.
Which gun you shoot will depend on how any particular scenario is set up. It might be pistol, pistol, rifle, shotgun. It might be pistol, rifle, pistol, shotgun. It might be just about any combination, depending on how the stage designer set up the scenario. Generally speaking, when you shoot a pistol, you will fire all five rounds and then holster the empty pistol. Then you do what ever is next. If your second pistol is next, you will usually empty it, then holster it and move on to the next gun. There are of course exceptions, but that's how it's usually done.
Traditional is the category where you hold your pistols with both hands. Yes, it is a misnomer, let's not go there. Duelist is where you hold your pistols with just one hand to fire them.
How you carry and draw your guns is not necessarily related to how you shoot them. I always carry my guns in my cross draw rig and shoot them duelist. Which gun I draw first will depend on the scenario and where I happen to be facing at the time. If I want to shoot my strong side pistol first, I draw it empty it, and holster it. When I shoot my 'crossdraw' pistol I swivel my hips to keep the muzzle down range, reach across my body with my right hand, pull the pistol, point it down range while resuming my down range postition, empty the pistol,then swivel again to reholster.
If I wanted to shoot Traditional I would do all of the above, but I would be holding the pistols with two hands when I shot them. The difference is, with a cross draw rig, you need to postion your body so you don't break the 170. But you don't have to change hands when you pull the weak side pistol. With straight draw holsters, you don't have to do the swivel business, your pistols will always be poined down range. But you do have to change hands when you pull the weak side gun. You pays your money, you takes your choice.
Cross draw rigs seem to be getting out of favor these days, at least around here most shooters these days seem to be shooting a pair of straight draw holsters. The exceptinon is Gun Fighter, where they pull their guns simultaneously with both hands. There is also a minor variation of Duelist called Double Duelist. A Double Duelist will shoot his guns with either hand, but he only shoots one gun at a time and cannot have 2 loaded guns in his hands at once. So he will pull his strongside gun with that hand, empty it and holster it. Then he will pull his weak side gun with that hand, empty it and holster it. Or vice versa.
The other categories, Frontier Cartridge, Classic Cowboy, Modern, etc, may or may not impose restrictions on the way guns are carried and are handled. You'll have to look up the specifics, it is all their in the handbook.
I hope I answered your question about butt forward on your other post. As I said, some ROs will not allow you to do the Cavalry twist, but their is no official SASS rule against it. As a newcomer to cowboy shooting, I suggest you try either a rig with a pair of straight draw holsters or a cross draw rig and don't start out with the Cavalry Twist. It takes a lot of practice to get it right.
Also, on a technicality, there is no such thing in CAS as being DQ'd for sweeping yourself. You cannot break the 170 and you cannot sweep anyone else. That pretty much covers the gamut. You cannot be called for sweeping yourself, anybody who calls you for that is making up his own rules.
Thanks for the comments about my Colts, they are 2nd Gens, the long one was made in 1973, the short one in 1968.