To my uneducated eye, it appears that you have an early Military and Police revolver, also known today as a Model 10.
It looks fantastic--no boogered up screw heads, no dings, almost pristine from what I can see. If that is the original finish, you have a very desireable handgun.
If you shoot it, be careful. Don't overstress the old fella--use only factory .38 Special in it (and not +P!), or carefully assembled handloads with 158 grain bullets or lighter.
Invest in a Dewey coated rod to clean with, and I personally would only use Hoppe's. Ensure that you only use bronze phosphor brushes; look for one with the looped end rather than the cut ones.
A good gun begs for a good oil. I use and recommend Kano Microil; it is a purified oil used for sensitive instruments, available from
www.kanolaboratories.com.
Have an experienced gunsmith show you how to remove the cylinder properly. Kept clean and lubed, it should last for generations. And, keep solvent away from the stocks--you might want to consider investing in a set of replacement grips. Keep the originals safe.
Congratulations on inheriting a fine revolver! I adore older Smith and Wessons.
