If the frame says M-65-3 when you swing the cylinder out, that is your answer. The third engineering change to Model 65. A stainless steel .357 version of the Model 10, formerly called Military & Police until 1957.
This is a K-frame, originally made in 1899 for the first M&P. It is the basic .38-size frame. Don't shoot it much with 125 grain or lighter .357 loads, as these erode the forcing cone, and the barrel may crack at the flat side, underneath, where the barrel throat is milled flat to allow cylinder closure.
This is a very sound choice as a basic service revolver, capable of killing even a bear, with careful shot placement. (I am aware of at least two bears killed with such guns. One was in fact, just a .38 version of this basic gun, and it was a polar bear in a zoo. The other was a grizzly mauling a game warden.)
This gun has fixed sights, and you may need to experiment with different ammo to see what shoots best to the sights, as you personally aim the gun. But you can use this on snakes and small game, and it's a great house gun!
It may kick a little hard for you, if it has the original wood service stocks. Rubber grips will lessen the effects of recoil. I use Pachmayr Signature grips on my .357's of this size. With .38 Special loads, recoil isn't that big a deal.
The gun was made in .357 Magnum caiber; it wasn't bored out. You're fine in that regard.
Those bored-out guns were ill-advised attempts to get more power from larger (.44 frame) guns originally chambered in .38 Special. Those took a hot-loaded .38 called the .38-44 Heavy Duty, and preceded the first .357 Magnum in the 1930's. Those haven't been made since the mid 1960's. I guess that folks realized that if they were carrying that much size and weight, they might as well have the same basic guns in .357. (Models 27 and 28.) However, the .357 models used a different steel alloy, with improved heat treatment. And they cost more.
Shoot the M-65 mainly with .38 Special ammo, and it will last well. Probably no more than about 10-15% of your shooting should be with .357 ammo. The gun isn't made to take continual .357 pounding. That's why S&W developed the larger L-frame guns. But the K-magnums are handier, and stand up well with moderate magnum use.
If this gun is in good condition, I think it'll last you for many years, maybe a lifetime, and I think you'll grow to like it a lot!
Note: Model 65 is ONLY a stainless steel .357 gun. NO worries about it being just a nickel finish. The blue or nickel version was called Model 13.
T-Star