S34903 was made in 1980.
You have a later version Detective Special with the heavy, shrouded barrel introduced in 1972.
These later steel framed models were factory rated for "up to" 3000 rounds of +P ammo, at which point they were to be sent in to Colt for inspection and possible frame replacement.
Since Colt no longer has any frames, you'd be best to shoot mostly with standard .38 Special ammo, and load up with +P for carry.
The Colt's made after WWII used letter codes to ID the frame models. The steel frame Detective Special was the Colt "D" frame.
In 1966 in order to simplify production, Colt began making all small frame revolvers with the "stubby" type grip frame that used grips that over lapped on the bottom.
Your Colt probably left the factory with the later Colt "Combat" grip. The rubber Pachmayr grip with Gold Colt medallion was heavily used by a lot of Colt owners, and in later days it was shipped with the rubber grips.
Here's what your Colt probably had originally:
The Detective Special was introduced by Colt in 1927 and immediately became THE detective, under cover, off duty, and concealed revolver for most police and civilians.
It was so popular, virtually every cop in America owned one, and it was so popular with police it became known as "a cop gun", and virtually identified the owner as a policeman.
It was so dominant in the market, S&W didn't bother introducing a competing gun until the Chief's Special of 1950.
The Detective Special was always known as the highest quality, most accurate "snubby" revolver ever made, and it was about the only one made that held six shots.