OK.....that nails it down.
What you have is the Model 1895 New Army and Navy
. Yours is the civilian version.
Those numbers on the butt are the serial #. I'd need that to tell you the manufacture date. The 1689 numbers are assembly numbers.
The caliber is .38 Colt.....NOT
.38 Smith & Wesson or .38 Special. .38 Colt is no longer made by the major manufacturers, but is loaded by some of the "Cowboy Action" ammo makers such as Black Hills Ammunition: http://www.black-hills.com/cowboy.htm
: If you plan to shoot this fine old gun, please
have it checked out by a gunsmith to make sure it's safe to shoot!
To clean the barrel & cylinder, do as you would do with a modern gun.
To clean up the surface rust, get some 0000 steel wool and some good gun oil (such as Hoppe's or Rem Oil), put some oil on the steel wool, and very lightly
go over the rusty spots. Do a little at a time, then wipe the gun down with a soft rag (old tee shirts work great)....make sure you're not taking any of the bluing off. When you've removed most of the rust, just give the whole exterior of the gun wipedown with a light coat of gun oil.
If the interior lockwork needs cleaning & lubrication (and it probably does), best leave that to the gunsmith.
That's a fine old Colt you have there.....have fun!