Back in business, typing one handed.
Corndog07:
You probably have a .38 Military & Police Model of 1905 4th Change manufactured between 1915 & December 1920. Serial range for those years was 241704 to 358xxxx.
Your gun predates heat treatment of cylinders, so stick to standard velocity lead ammunition only. Avoid jacketed, plus p or +p+ marked ammo you don't want a bulged or cracked cylinder.
Your gun also predates the positive internal hammer block safety introduced during WWII. If dropped on the hammer it could fire, so leave the chamber under the hammer empty if you keep the gun loaded.
Some target models were made without the S&W logo, some had the S&W markings only on the barrel. There is the small possibility that you have a cheap Spanish copy which may be unsafe to shoot, I recommend you post pics of both sides of the gun for a positive ID.
The original grips would have been hard black rubber or walnut. The rubber grips are prone to cracking with age, so it isn't unusual for them to be replaced.
Value is not high as there were millions of M&Ps made, $250 to $350 is normal for a good to very good condition gun.
http://www.gunpartscorp.com/ is your best source of spares.