Very nice gun and in excellent condition. I, too inherited one from my father. The guns are not rare at all, although your 6" barrel is probably rarest of the lot, but literally millions were made.
Since you're new to 32-20, I want to warn you about vintage ammo. For many years, Winchester and Remington made a "rifle only" 32-20 cartridge for use in the Winchester lever guns (1892 I believe). If you come across these (most likely at a gun show or something) DO NOT use them in your revolver. I believe the Remington brand will be marked "Hi-Vel" or "High Velocity" or something. These rifle only loads will generate pressures beyond what your revolver was built for.
Any commercially made ammo you might buy from a retailer today is good to go. Good luck finding ammo in the current mess. I you shoot it a lot, you'll want to reload. Watch the case mouths for damage during the reloading process. Use the lighter/starting loads to save wear/tear on your gun.
They're fun to shoot, although I find the grip bites my knuckles when I shoot it. A Tyler T-Grip helped (order on for any Colt D Frame) some. I've taken a few grouse with mine while out moose hunting, but I no longer carry it in the field.
The 32-20 was competitive, ballistically speaking, with the 38 special of the day, but not with modern 38 ammo.
You can go to
http://www.proofhouse.com/index.htm and type in your gun's serial number (under the crane IIRC) and get the year your gun was made.