Hiya K1ger, and welcome to the forum. There are a lot of people here that are more knowledgeable than me with these old shootin'irons, but I'll explaterate to the best of my abilities:
Yours is a K-frame .32-20 Hand Ejector model 1902 (Second Model), distinguished by the straight barrel shank where it screws into the frame, the round butt, and the ejector lug under the barrel; mfg'd 1902 - 1905 (distributed GKW); approx.4,500 of them (1902 2nd's) made. There were around 7 variations on 32-20's made,and they were manufactured up until 1940; I think there were around 150,000 32-20's made in total. They were popular with trappers and hunters, and most have seen a lot of hard use; there are very few sock-drawer 32-20's around these days.
The 32-20 (AKA 32 Winchester), was popularized in folklore and also in some old blues songs (Robert Johnson, no less) as "the boollet that'll shoot right-straight through a man". In that regard we are often warned NOT to shoot 32-20 rifle cartridges in these handguns, and that warning would be especially true in a gun mfg'd before the mid 30's when metallurgy was somewhat improved. Regardless, 32-20 ammo is uncommon and expensive. If you're going to shoot your inheritance, you should learn to reload if you don't already do so. Best advise: keep them mild. I've got a couple of them (an 1899 1st, and a 1905 4th) and I find them very pleasant to shoot and also fairly accurate.
Your gun appears to have fixed (service) sights, as do most of them. They made a few target sighted editions in all model forms, but I've never seen one. Regarding value; in your case since it came from your father's estate: priceless; don't ever sell it (best advise that I wish I'd gotten a couple of decades ago). They are fairly common and when sold they tend to go for around the same money as the k-frame 38 spl's, if not a little less due to ammo availability.
Hope this helps -S2