'Snowman' - BAR pretty much covered it.
U.S. Model 1896
Krag, #51840, was built as a rifle around December, 1896, or January, 1897. Long ago, a Civilian turned it in to a Hunting Rifle.
Your barrel is a 1903 Springfield barrel that was shortened at the breech, re-chambered to .30-40, re-threaded and fitted to your model 1896 action. This was an old gun-smith practice to cheaply replace a poor barrel. The Springfield barrel has a smaller diameter, different taper, and lacks Krag rear-sight holes.
IMHO - There is nothing practical to restore here. Your best course is to try shooting it, as is, and see how it performs. If you are satisfied, then there is no harm in stripping the paint, refinishing the metal and wood, and fitting a new butt-plate. Do it yourself because it will not increase this Krag's value. ($175-200 AND POOR 'RESALE' PROSPECTS').
An old Pacific or Redfield 'No-Drill' Peep-Sight could be put on it and improve shooting.