Welcome to the Forum. You have a 2" K frame .38, numbered the model 10-5 but also named the .38 Military & Police as the top of the parts sheet notes. These came in blue and nickel finish, but as you note the metal of model 10s of this era were not highly polished. However, if you use a metal polish (no heavy abrasives and light pressure) you may be surprised as to how shiny it may look.
The D 870000 on the bottom of the grip frame is the SN, and puts it as an early 1976 ship date (the factory tracks by this and not production). It has the so-called 3-screw frame, all of which you can see on the right side (plate) with the stock panel removed.
Finally, if the ammo with the gun is round-nosed, they are probably 158 gr standard pressure, which was the police service load for decades. For a first target shooting session, this type of round should work fine. You will probably also see for sale 130 gr FMJ and 148 gr wadcutter rounds that are easy to shoot.
I think you owe someone dinner, at least
. Hope this is helpful, and let us know how it shoots.