First, congrats on a great find and a better deal. The Model 36 Chiefs Special is quite a common gun, but it is also a very good one too.
Tidbits:
First "J" (small) frame revolver, created for the .38 Special by up-sizing the existing I-Frame.
Introduced in 1950. Original had a round trigger guard, tapered round barrel and a half-moon front sight.
By 1953, a slight redesign took place. The trigger guard was now oval, a ramp front sight was installed and the grip frame resized, starting the "typical' Chiefs Special look.
It differs from most S&W designs by using a coiled mainspring in the grip instead of a flat leaf spring.
Production ended in 1999.
Throughout it's lifetime it was rarely modified. Prior to 1957, two changes deleted the trigger guard screw and upper sideplate screw (hence there are 5-screw, 4-screw and 3-screw variants).
Designated Model 37 in 1957 when model numbers were assigned.
Made in both the round-butt grip (like yours) or a square butt for the 3-inch barreled versions.
The 36-1 refers to the "Heavy Barrel" variant.
The heavy barrel was made standard in 1975.
The pinned barrel was eliminated in 1982.
The Model 36 spawned a stainless steel version in 1965. This was the first production revolver in stainless steel (as the Model 60) and a ground breaking change in the industry. In 1970, due to the success and popularity of the Model 60, S&W announced stainless steel versions of other models.
Sights are factory regulated with standard velocity 158 grain RNL ammo.
Your gun should handle +P ammo just fine, though it will accelerate wear on some of the parts.
The short barrel loses velocity for a given cartridge. Some early +P ammo was created to help the "snubby" guns reach or exceed .38 Special standard velocity from the short barrel.
Some police detectives found that the 148 grain wadcutter bullet, though slow, was effective at 7 yards. For a short time one could buy High Speed wadcutter loads for duty use.
In the early 80's, Federal's 125gr +P Nyclad LSWC-HP design was considered very effective. Today's Nyclad is standard velocity and uses a different HP design.