Well, the 1851 Navy is kind of the standard gun in that caliber. It's a favorite for many of us on this board.
The 1861 is also a tremendous gun, technologically superior to the 1851. The look is different, as is the grip. I would handle both, if you have the opportunity, to see which one feels better to you.
I have a real soft spot for the '62 Police model. It is smaller than the Navy guns, more along the lines of a modern revolver, and is a real delight to the hand and eye.
The 1858 Remington is also a very good choice for the newbie. In my experience they normally are more-or-less ready to go out of the box, which can't really be said for the Colt pattern guns. And they can be had from the factory with usable sights - even adjustable ones, if you want. The downsides are the small diameter cylinder pins, which can gum up more easily than the Colt's, and the grip shape, which many find a little odd and uncomfortable. Again, a good idea to try before you buy.
Beyond gun choice, you will encounter two main brands: Pietta and Uberti. In my opinion both are about the same quality and the same price (although the Piettas are more often found at fire sale prices from the big retailers), and both usually need a bit of "fixing" out of the box. Ubertis are well known for having a too-short arbor. This is not the end of the world, especially if you shoot only occasionally, but really ought to be checked and fixed. Full details on the process are easily found with a search on THR.
Piettas have a reputation for cylinder bolts being too wide, as well as timing problems. Those are troubles which, if present, really need to be fixed before the gun is used. Again, not a huge deal, and lots of information to be found here and elsewhere. Pietta also sometimes takes some flak for not being "authentic", ie. producing models which never existed historically. This really bothers some people, but I'm not quite sure why. My personal quibble with Pietta is the way they write all over the guns with the brand, model, serial number, proof marks, or whatever else they can think up. And of course, there are lots of people who've gotten guns from both manufacturers and used them happily without ever needing to do anything at all to them!
Finally, you should be aware that the sights on these guns are, by today's standards, awful. With your young eyes you should be able to manage them, but it is a lot tougher than it should be, and most of these guns hit very high at "normal" handgun ranges. I normally file a dovetail for a blade front sight and cut the hammer "V" into a square notch. This makes the guns much more usable, but deeply offends a certain kind of shooter.
Anyway, sorry for the long post. I literally have nothing else to do, thanks to Governor Newsom!
