Note that by "initial function check," I meant that I took it to the range and fired it with the factory iron sights. I knew I wouldn't like them, but wanted to make sure everything else on the rifle was working properly.
As far as what tang sight you might want, that depends upon what you intend the rifle's primary use to be. My 1873 short rifle wears a Montana Vintage Arms (MVA) copy of the Marble's flexible tang sight, and a Beach combination front. That should be a fine hunting sight, and should be very good for any type of Cowboy Action Shooting. I will mention that I routinely replace factory rear barrel sights on my lever action rifles with a Marble's 95 folding leaf rear barrel sight rather than a slot blank. The latter sight is historically appropriate for all lever action rifles from the 1873 onward and gives the shooter the option of using an open barrel sight if such is wanted.
On the full-length rifle, I installed a globe front and, after buying an MVA vernier sight base, installed one of the firm's least sophisticated vernier sight staffs that I happened to have on hand. That tang sight proved unsatisfactory, and I soon ordered a Soule mid-range staff to replace it. I intended from the start to use that rifle to fully exploit all the accuracy and range I could get out of a .44/40 in match shooting, and the sight arrangement has not disappointed for that purpose. With a post front sight insert, it could certainly be used for hunting, although it might very well prove awkward for close-range snap shooting. While I am not a Cowboy Action Shooter, I think this sight arrangement would prove miserably ineffective for any scenario in that discipline.