For a first-timer, I suggest a Remington .44 caliber revolver.
Why? Because the larger balls needed for best accuracy are readily available. This means balls of .454 or .457 inch, not the oft-suggested diameter of .451 inch.
Now if Speer, Hornady and Remington --- the most commercially available brands of balls --- offered a .380 inch ball for the .36 caliber sixguns, I'd have no qualms about suggesting that caliber. As it is, they only offer balls of .375 inch diameter, which I've found too small.
If you cast bullets already, and have a good source of dead-soft lead (at least softer than wheelweights) then you can get a Lee bullet mould of .380 inch and make your own oversized balls.
If you search the internet, you may find .380 balls for sale. Warren Muzzleloading of Ozone, Arkansas once sold them. Then its site was down. I just checked and don't find it anymore. However, there may be others out there that offer .380 inch balls.
But for a beginner, all you need is readily available if you buy a .44 caliber revolver. I'd suggest the Remington as it's authentic --- Colt never made the 1851 Navy in .44 caliber so it's not authentic. Because of its smaller cylinder, intended for the .36 caliber, it will not hold as much powder.
The Remington is also readily available in stainless steel; at the moment I don't know of anyone making an 1851 Navy in stainless steel. Colt did back in the 1980s but those now bring premium prices and are not easily found.
For a beginner, I'd suggest a stainless steel Remington in .44 caliber. You can get target sights if you wish but I think you'll find it more fun to leave it authentic and use the fixed sights.
I suggest stainless steel because beginners are often not very conscientious about cleaning their cap and ball revolvers as they should be. Stainless steel is more forgiving.
I'd suggest using real black powder, in FFFG grade if you can get it, and a hard felt wad soaked in Gatofeo No. 1 Lubricant twixt ball and powder. You can purchase Gatofeo No. 1 Lubricant and hard felt wads soaked in it from Big Iron Barrel Works at
http://www.bigironbarrels.com/.
See my posts above, concerning cap and ball revolvers. You'll find a lot of good information in there.
You'll want to print out the above posts; I'm a long-winded ol' desert cat.
One last word: Never, EVER use smokeless powder in your revolver. Sooner or later, someone will suggest you put a pinch of Bullseye, Unique, W231 or some other fast-burning powder next to the nipple, before adding the black powder.
Don't do it. That person is a fool.
Use nothing but black powder of approved black powder substitutes, such as Pyrocex or 777. Note too that Hodgdon 777 should not be used at the same volume as black powder or Pyrodex. A visit to the Hodgdon website will offer 777 loads.
Should you choose to purchase a cap and ball sixgun, you'll find yourself in a fascinating hobby. It's great fun to stoke one up, touch off a shot and find a link to the old-timers.