First, this looks to be a four screw gun. The upper sideplate screw was deleted in 1955. Model numbers began to be stamped inside the yoke in 1957.
If you have no Model number inside the yoke, then you have a pretty close approximation of the revolver's date of production. If you have a Model number, you know it's a post 1957 gun. If there is no screw in the triggerguard, it's a post 1961 gun. The dash numbers should also help date a post 1957 gun.
edited to add: Serial K 311XXX would make it a 1957 gun.......Duh........
The grips are likely originals, with a serial number stamped inside. There should also be a serial number on the flat under the barrel, and the rear of the cylinder.
It's difficult to judge finish wear by a photo, bt your revolver looks to be at least a Very Good. That places it at $425 if it's a K-22 Masterpiece (pre 1957) and at $350 if it's a Model 17 (post 1957). FWIW, the Model 17 is also recognized as a K-22 Masterpiece. These price estimates are from Supica's
Standard Catalog of Smith & Wesson, 3rd Edition.
edited to add: Being a 1957 gun, your gun's basic value will be determined by whether it bears a model number or not. Final value determination will be made, as always, by a purchaser's willingness to pay the price.
In use, this will be a highly accurate and fun revolver. The best part about this gun is you apparently already have some muzzle wear. The worst depreciation is over. Enjoy it. Shoot the snot out of it. I love mine!
FWIW, I paid $199 for mine, a Model 17-3, last year. Yeah, I was happy!