LMH, I'm not a competitor, so take this with a grain of salt. I've been around a lot of cowboy action shooters, talked to quite a few, read about it a lot and shoot the same guns. I am basically into the old west guns but for a number of reasons (probably the foremost being I am anti-social :), I'm not active in the game).
It all depends on what your aim is. Are you interested in the gaming aspect of it or are you more interested in history and costuming. A few years back I know it was common to give prizes for the best attire...most original, etc. Also sometimes the prizes were drawn rather than awarded to the top people. The gaming aspect has definitely evolved but I know that many shoots, especially local ones, still stress safety, etc. No fast draws. All these things obviously will impact what your equipment is.
You also have several categories. Competitors please correct me, but basically you usually have Modern, historically-correct and black powder. The moderns can be about any SA, with Blackhawks dominating. The historically accurate category (and I disremember the exact terms so mine are kinda made up), allows SA's that look like the old guns or the old ones themselves. They don't have to be exact, but they pretty much appear that way. No Blackhawks, but Vaqueros or New ones are fine. No double-actions, even if they are really antiques that were used back then. In the last category, you have cap and ball guns. You may have load restrictions so you are not blowing the crap out of the targets too, so be advised of that.
Your '94 should be fine. If it's not, you'll know. lol I agree with the Vaquero. The .357/.38 is not a traditional cartridge but is widely touted due to its lower recoil and ability to acquire targets quickly. The 32-20 does the same thing and is authentic, but is harder to come by both in guns and ammo. Either can be had in both handgun and long gun in order to simplify loads. If you want to use the .44 Mag. you could use a 50th Anniversary Blackhawk. I don't know if the more common Super Blackhawk is allowed. The Super Buckhorn by EMF used to be seen once in awhile. I don't know if it is still available new.
Anyway, this gets involved quickly.
You'll need a scattergun too.