Welcome to the forum. Nice .32! They don't always look that good when they are that old.
I think the factory would have called that a 3.25" barrel; the basic barrel lengths for the early I-frames were 3.25", 4.25" and 6".
I have had good luck shooting wadcutter target ammo in these old .32s (1920s and before). I have been using Sellier & Bellot ammo, which is a little dirty and smells funny, but it makes nice clean holes in the targets. You can buy it from internet distributors. I think Fiocchi makes some good .32 wadcutter rounds as well.
Some people just like regular roundnose ammo and find it more accurate than wadcutter rounds.
If you shoot it, please post a range report.