Welcome from Virginia
Welcome from Virginia! You have received one of the finest guns that S & W ever made. There are several things that are needed to place a value on your gun. If you have a sales receipt, or the box that it came in, tools (cleaning rod, brush, maybe a screwdriver (SAT)) and any documents/warranty card, etc. these extras also add value, especially if the end tag on the box matches the serial number of your gun.
So......things needed to be known (cell phone pics are good for posting).
Serial number: stamped into the butt of the gun frame (see pic of my 1952 "pre-Model 27). Yours may have the S prefix like mine because the Model 27 did not change to N prefix until 1969.
Next is number of screws, counting the ones you see on the sideplate, plus the hidden one under the right grip, plus the trigger guard screw. These are known as 5 screw revolvers.
The gun was marketed as ".357 Magnum" from post WWII (1947 until 1957). In 1957 S&W started stamping Model numbers into the yoke area of the frame.
In 1960 The Model 27 was stamped Model 27-1 which indicated that the extractor rod thread was changed from right hand to left hand thread.
In 1962 another engineering change, designated Model 27-2 changed the cylinder stop and eliminated the trigger guard screw and in 1968 the diamond center grips were deleted. Finally in 1969 the serial numbers were changed to an "N" prefix.
So you see that some simple cell phone pics will help us to assist you in pinning down your gun. Since you are pretty certain you have a 1961/1962 gun.... the value can be hard to ascertain because if for example it turns out to be a Model 27 with no dash, or even a Model 27-1 (only made for a year) these may bring a substantial premium over Model 27-2 which are still quite valuable in their own right.
Also the exact condition of your gun is a main and over-riding factor when selling. If it has been treated decently over the years and only shows light bluing loss at high points that's great, but if its' rusted and/or pitted that would be a major problem.
Some examples from my collection shown below:
"Pre-Model 27", s/n S 84926, 6-1/2" bbl, diamond magna grips, shipped October 16, 1952
Model 27-2, blue, 3-1/2 bbl, shipped April 5, 1977
Model 27-2, Nickle, 6" bbl, May 8, 1980, with original blue box, tools, documents.
As to value, I have not seen any Model 27 or pre-27, go for less than $1,000 in over 3 years unless it was a worn beater. Most are bringing more than $1k, and if scarce...a lot more than $1k.
The 27-2 with 3-1/2" barrels are crazy priced right now with $2,500 to $3,000 not unheard of on the GB big auction sites.
So show us, or tell us what you have and we will gladly assist you. Since your gun is an inheritance you may decide to keep it, and shoot it...they are very accurate guns and fun shooters.
Let us know what you have when you can.