The Ruger Old Army is the one to get for reliable, trouble-free shooting. It's expensive, however, and not at all "authentic." It's a modern cap-and-ball sixgun that just kinda looks sorta mebbe a little sumthin like a Remington New Model Army.
In the replica category, the big three are the 1851 Colt Navy, 1860 Colt Army and the Remington New Model Army (often referred to as the model 1858, which is a misnomer -- it actually came out in 1862 or 1863).
All three have their advantages and disadvantages. The 1851 Colt is a real classic. It was one of the first true personal handguns that worked, and it worked well. They were made by the hundreds of thousands. Wild Bill Hickock carried and used a pair to legendary effect. They are extremely well balanced. The .36 caliber (actually .375) ball is very soft shooting and gets good velocity.
The 1860 Army Colt is just a beautiful pistol. The smooth lines of the loading lever are a sight to behold. It is more powerful (.44 caliber -- actually .451) and its larger grip frame fits many shooters' hands better.
Both of the Colts have open top frames. The advantage is that they are very tolerant of fouling and take down easily for cleaning. Just remove the wedge and the major pieces (barrel, cylinder, frame) come apart. You can easily clean the barrel from the breach end.
The disadvantages of the open top Colts are: (1) the wedges tend to loosen over time, especially under heavy loads; (2) they are inherently weaker than full framed guns; and (3) the rear sight is a notch in the hammer, which is necessarily tiny and susceptible to movement or damage.
The Remington NMA with its distinctive wedge-shaped loading lever and top-strap frame was revolutionary. The replicas can be somewhat sensitive to fouling between the cylinder and frame, however. They are large pistols, like the 1860 Army. The grip frame has a different shape, however, that you may or may not like. I have large hands and find that the Remingtons fit my hands better than the Colts, but people with smaller hands tend to prefer the Colts (especially the 1851 Colts).
In terms of manufacturers/brands, Ubertis used to be considerably better than Piettas, but the Piettas I've seen in the last few years seem to be as well made as the Ubertis. I have had the pleasure of meeting Alessandro Pietta, and he told me that his company has indeed made great strides in quality control. That being the case, I no longer see any reason to pay a premium for Uberti-made guns. You will still find some from both Pietta and Uberti that didn't get the attention they should have had, but the odds of getting a good one seem about equal for both companies.