35 Rem is right. That's a standard 'Carbine' barrel sight. A "Vernier" sight is usually mounted on the tang with a screw adjustment to elevation and sometimes with a windage adjustable base.
In my experiance, in order to get the most accuracy out of an iron sighted lever gun, you need a Lyman 66 reciever sight and a fine (1/16") gold bead.
These are meat guns and they do alot of killing every year at ranges up to 200 yards.
Given that your NRA Musket is already drilled and tapped you are halfway there already....