These fellows have given some excellent advice. You have to remember that if you are going to stick to original designs, they aren't going to have adjustable sights or anything close to it. On your semi-autos you have a lot of options and usually some sight adjustment as you well know. It's a whole different story in the SAA. You're utilizing a fixed front sight and usually a groove in the top of the receiver - not a whole lot different from more modern designs such as say a Colt Army Special/OP or similar. On the older Colts - the '51/'61 Navies or 60 Armies, you're utilizing the front sight and a notch in the hammer due to their open top design. It's just a different animal and the "nature of the beast".
The trick is to learn the individual pistol and how/where it shoots. Adjustments can be made in sight height but not always easily depending upon the make and how it's installed. Windage adjustment on a SAA was often taken care of by a slight bend in the front sight in the right direction to correct it.
i don't shoot competition but I do enjoy the SAA styles. For me, I enjoy my New Vaquero the most. Would a true Colt shoot better? Maybe. Would a Uberti? Maybe. If you buy a new SAA will it shoot "right on"? Maybe or maybe not. Will one brand shoot better than another? Can't say. But then again, if I buy a semi-auto will I be guaranteed it will shoot great right out of the box? No.
As stated, the best way to decide on one is to handle them in person if you can and see which make/model fits and feels good to you and what barrel length feels balanced and natural in your hand. Then, take the plunge and try it. Again, they are a whole different animal from something like a 1911 or whatever semiautos you have your experience with but I have a feeling that if you already have the "itch", you will enjoy them. Notice I say "them" as they soon become "addictive". Good luck on your new "journey" and above all, enjoy and have fun!
If a pair of '51 Navies were good enough for Billy Hickok, then a single Navy on my right hip is good enough for me . . . besides . . . I'm probably only half as good as he was anyways. Hiram's Rangers Badge #63