Several have mentioned that the Colt may be out of time. It probably is, but, so what? Such a condition is common on old Colts, but generally has no effect on shooting, and certainly has no effect on the collectability of the revolver.
My answer to these Colt versus Smith & Wesson timing discussions is that, yes, double action Colt revolvers do go out of time with extended use, but double action Smith & Wesson revolvers are always out of time!
The common Colt double action design (as introduced in the 1898 New Service and the 1908 Army Special, and finally ending with the Python in 2006) is such that, as the trigger is pulled, the cylinder is rotated tightly against the cylinder stop, eliminating ALL play in the cylinder at the moment of firing. The hand is what applies the pressure to the cylinder to hold it against the cylinder stop (the bolt), so the shock of firing causes wear on the hand. The wear on the hand will slowly progress to the point that the hand will not rotate the cylinder into final lockup if the hammer is cocked slowly. However, pulling the trigger will always force the cylinder into tight lockup at the moment of firing, so the worn hand really has no effect on function of the gun at the moment of firing. Inertia from more rapid cocking will also carry the cylinder into preliminary lockup with the bolt in the cylinder stop notch even before the trigger is pulled and the hand applies pressure to the cylinder.
On the Smith & Wesson double action design as introduced on the Military & Police in 1899, the hand does not lock up the cylinder at any time, and does not take the shock of firing. The cylinder is free to "float" at the moment of firing, held only by the bolt in the cylinder stop notch. The amount of play in the cylinder varies from gun to gun. (Older Smiths tend to have less play.) The only Smith I have that does not have play at the moment of firing is an early Triple Lock, which is about the finest fitted firearm I have ever seen of any brand. The cylinder on every other Smith revolver I have has some play at the moment of firing. The Colt Mark III/V action is like the Smith action in that the hand does not apply pressure to cylinder at any time after rotating it into firing position. (The Colt Mark III/V action is actually more like a Ruger action since it uses a transfer bar ignition system.)
This lack of play in a Colt at the moment of firing is said to be the reason for the generally superior accuracy of a Colt revolver. Replacement of the hand on a Colt from time to time is the price paid for the Colt "bank vault lockup" system. A Colt hand can be "stretched" by peening and, if done properly, can double or triple the life of a Colt hand.
When considering near century-old military revolvers as collector pieces, with occasional firing for recreation, the timing issue is irrelevant. Buy the Colt and then buy a Smith & Wesson when you find one. Keep both as examples of what America did to arm its soldiers in the Great War.
Now that that is settled, you can begin your search for the accouterments that are needed to make your Model 1917 collection complete! Good luck.