Hard to tell for sure, but it sounds like you might have a model 17 or model 18. Use the thumb-piece on the left side of the frame to open the cylinder (holding the weapon in your right hand, use your right thumb to press the thumb-piece latch forward, toward the end of the barrel, and hold it, while rolling the cylinder out of the frame with your left hand). Look on the now-exposed cut-out part of the frame under the rear of the barrel, see if there is a model number stamped there (might say something like "Mod 17-2").
If it's a model 17 or 18, it should be a blue-steel six-shot revolver. The barrel on the M18 will usually be 4 inches; the M17 had a 6-inch barrel (measure from the front of the cylinder to the end of the barrel to get the correct measurement). Usually this model did not come with horn/stag grips, but it is fairly common for revolver owners to replace the grips to personalize the weapon or make it fit their hand better.
Pretty much any S&W .22 revolver in decent condition is worth $275-$300, but it might be twice that amount, depending on options and exact condition. Be aware that if you try to sell it to a sporting goods store or pawnshop, they will only offer you about half of what they think it is worth, so they can sell it at a higher price to cover their expenses and make a profit. That is how they pay their employees, keep the lights on, and the doors open.
The below photos may differ from your gun in the sights, trigger/hammer shape, and the color and appearance of the grips, but everything else should be fairly close.
A S&W Model 17 w/6-inch barrel:
A S&W model 18 with a 4-inch barrel: