I haven't replied to this, mainly 'cause I wanted to see what everyone else had to say on the subject before I did.
A fixed sight '58 Remington is much easier to hit with than ANY of the Colt open top guns, due to the differences in the sighting systems. Once you get used to the sights on a Colt though, you've shot it enough to probably ignore the sights anyway and "point-shoot".
Some people like the handling of the Colts better and if I had to choose?--The 1858 Remington makes a better target/hunting gun and the Colt 1860 Army makes a better close range combat gun. The long grip handled ("4 screw frame") 1860 Colt Army is the best "pointing" of the revolvers, especially if you have bigger hands. The Colt Navy is better in a smaller hand, and you can have it in .36 caliber. You can also get the '58 Remington as a Navy model in .36 caliber and with a shorter barrel, which is a very nice handling gun also.
As far as accuracy for hunting and targets, the single shot .50 caliber Traditions Trapper is an excellent gun. It has double set triggers and adjustable sights. Traditions also makes the Pioneer Pistol in .45 caliber and the .32 caliber Crockett Pistol which are more simple in design. The Lyman Great Plains Pistol can be had in .50 or .54 caliber, so it packs the most wallop for larger game. It is also a very good shooter despite the primitive style sights.
A Colt Walker or the Colt Dragoons are VERY heavy and were all meant for use on horseback--not intended to be carried on belts. They don't lag too far behind the single shot pistols and in some rare cases actually can exceed them in power. Depends on the caliber and how much powder it can safely be loaded with according to the manufacturer.
As far as cost goes, you are looking at similar pricing for a single shot pistol a typical revolver. So if you've really got to keep the cost down, there's not going to be too much difference initially. BUT, you will need to buy some additional accessories for the revolver though. Won't get into that right now, but that could affect the total overall cost of choosing the revolver.
There is a neat flintlock pistol from Deer Creek products that is basically a copy of the CVA .45 cal. Tower pistol. It has a rifled barrel but NO sights though. This is more of a fun piece than practical--except for close range duels.
The single shot pistol kits are fairly straightforward to assemble if you're mechanically inclined. A revolver kit can be tedious and frustrating, or it might just need polished and final finishing, they vary in that respect. If it's your first handgun, I'd stick with a finished pistol or revolver than a kit though.
Since you have a rifle, you already know how to load a single shot pistol. Likewise if your rifle is flintlock and .54 cal. then logically the best choice would be to get a flintlock pistol in the same caliber. Likewise if it's percussion and .50, or whatever combination of lock and caliber... stick with the same in the pistol.
Loading the revolvers is a whole different "ball game". You don't use patches as in the rifle or single shot pistol. The ball is slightly oversized for the revovler chambers, whereas the ball is slightly undersized for the bore in your rifle. You also should seal the chambers with grease or use a lubed wad between the powder and the ball in each loaded chamber. The caps can fall off sometimes from recoil, the cap fragments can sometimes fall into the inside of the frameworks and jam up the revolver too.
You also already know how to clean a single shot pistol, which is the same as your rifle. The clean up on a revolver is not difficult, but is more involved and can require disassembly. The internal works are quite fragile and the springs in a revolver can break easily especially from a cap fragment in the wrong place. There's also a bizarre phenomenon called a "chain fire", or "multiple discharge" that can occur with a revolver. Currently one of the hottest threads in this section is on theorizing what actually causes it to happen. I wouldn't let that affect your choice though.
Anyway, I'm not trying to change your mind about the 1860 Colt Army that you seem to have made your decision on. Either the Pietta or Uberti will be a nice choice. The price will be different too. Make sure you get the steel frame, "4-screw" long grip model.
That's enough out of me, huh? Make sure to let us know what you end up with, OK?
Shoot Safely!
WV_Hillbilly