Based on your criteria sounds like a lever 30-30, Winchester / Marlin or new Mossberg would work for you as others have recommended.
ammo choices:
55 grain Remington accelerators get the small game thing done, and shoot fast & flat.
Standard 30-30 ammo can be had relatively cheap especially right before hunting season, good to 200 yards.
Hornady LEVERevolution 160 grain ammo, zeroed 3" high at 100 yards drops -.2" at 200 yards and -12" at 300 yards with 1000 ft lbs of energy left.
Self Defense load:
Federal 125 grain or better yet.
Remington's new 125 grain reduced "managed recoil" load, 2175 fps at muzzle & 1330 ftlbs, 900 ftlbs at 100 yards.
thats a lot of versatility in a 100 year old design.
a lever action in a pistol caliber would be good also, although costing you a little more initially, but in 357 you would probably make that up in ammo costs if you plinked more than anything, and in the long term would probably save money, especially if ammo costs continue to rise in the future.
I'll throw another one in, the SKS. Good to 200-250 yards, cheap to get and cheap & fun to shoot. It would fill your bill on all fronts, although it's not from the 1800's.
Although some of the AR guys might think so
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L8R
W B