Ivery Johnson revolver???

It's .32 S&W/S&W Short, the cylinder doesn't look long enough to be able to chamber a .32 S&W Long. I'm not sure if it's black powder or smokeless, but it looks to be smokeless to me as the bolt stops are slots and not troughs and the owl is facing towards the grip, not the barrel.

Not many options out there for .32 S&W Short, Winchester, Remington, and Magtech are about your only factor ammo options with Magtech being the cheapest.

You should have this inspected by a qualified gunsmith before attempting to shoot it. Many, if not most, of the surviving top-breaks of that era are badly worn and will have timing and or lockup issues which may render them unsafe with modern ammunition.

BTW, the name is Iver Johnson. The original company was in business for about 100 years, from the 1870's to about 1974. The name was purchased by others after the original company went broke, so guns are still sold under the Iver Johnson name today.

Judging from the pictures, your gun is made for smokeless powder so modern .32S&W ammo will be fine assuming the action works correctly. It is always a good idea to have an old gun checked out by a competent gunsmith before shooting it. .32 S$W ammo is somewhat less common than .32S&W long which won't work in your gun so look carefully at the ammo before buying.