Chris called it: it's a K-frame .32-20 Hand Ejector. You can tell by the stamp ".32 WINCHESTER CTG." on the barrel. The I-frame .32s (and the later K-32 Masterpieces, which are almost all postwar) are chambered for the .32 S&W Long.
The serial number puts it about 1907. Looks good for a century old.
The company made about 144,000 in this caliber before suspending manufacture before WWII. Most were fixed-sight guns, and the adjustable sight versions command a premium. This one looks to be in pretty good shape, apart from the blueing loss on the barrel. Stocks are nice.
The $600 offer is about right for this gun with fixed sights, or maybe slightly generous. But the target version should bring a 50-100% premium, according to the Standard Catalog of Smith and Wesson. My thinking is that you ought to get at least $900 for it from a collector, and maybe a little more.