You have a .38 Military & Police Model 0f 1905 1st Change manufactured between 1906 & 1909 in the serial range 73251 to 146899, so 1906 seems likely.
The caliber is .38 Special, also known as .38 S&W Special and is readily available at any gun shop. The .38 Special case is simply a stretched .38 Long Colt case, so both will chamber in the gun. If you shoot .38 long colt you will get a build up of lead and carbon in the cylinder chambers as the case is shorter than the chamber. .38 Long Colt is pretty much a specialty round for shooting in antiques and will be hard to find and costly, so there is no point in buying it. Stick to .38 Special.
S&W marked their guns Service Ctg because they would not stamp "Colt" on their guns. Colt played the same game, dropping the S&W part of the cartridge name when they chambered guns for .38 S&W .38 S&W Special, .357 S&W Magnum, and .44 S&W Magnum. CTH by the way is an abreviation of Cartridge.
Your gun predates heat treatment of cylinders, so avoid any PlusP, +P, +P+, jacketed or semi jacketed ammo. Use of these rounds could result in a bulged or cracked cylinder.
158 grain lead round nose or 148 grain lead waddcutters should shoot to point of aim and will as safe as any other round.
To check out the mechanical condition of your gun you can use this thread:
http://thefiringline.com/forums/showthread.php?s=&threadid=57816
Your gun also predates the positive internal hammer block safety. If dropped it could fire, so treat it as a five shooter, leaving the chamber under the hammer empty.
BTW, I'm the guy who answers the date of birth thread, so no need to re-post your question there.