As authentic as possible means black powder.
Too messy and corrosive for plinking, IMO. Bad enough with a muzzleloader, which is much simpler to clean. My cap-and-ball revolvers sit in a safe covered in oil, because I seldom get up the initiative to go shoot them, since I'll have to clean them right afterward and it's a PITA.
So, if you're not shooting BP, you're not "authentic." Therefore, might as well get a caliber that you can get in bulk for cheap.
Everything mentioned except .38/.357 is pretty expensive to buy off the shelf. So that would be my choice if I didn't have any particular plans for the gun (e.g. hunting big game).
On the other hand, those guns aren't cheap. Reloaders are a lot less than the price of one of them.
So my choice might be to budget a reloading setup in with the purchase, and just plan on reloading.
Then I'd choose an original round; anything but .45-70, especially since those guns have metal buttplates, and they all make fun volume-shooters. BTW I'd toss .45LC in with the others as a vintage round. It's readily available, but it's not cheap, so it's still a round I'd want to reload if I were going to shoot it much.
Something to note: some of those guns may not stand up to modern super-hot hunting loads (like the high-end .45LC that's hotter than.44 Magnum), since they're black powder designs, though they do have better, modern metal. So choose carefully if you plan to use the gun for big game, or get the .45-70.