Regarding CW era Colts, there were:
1851 Navy - .36 octagon barrel 6 shot
1860 Army - .44 6 shot round barrel
1861 Navy - .36 round barrel 6 shot
1862 Pocket Navy - .36 octagon barrel small frame 5 shot
1862 Pocket Police - .36 round barrel small frame 5 shot
I am not aware that the 1862 Navy was actually used by the USN. It is called a "navy" because of the .36 caliber as opposed to the .44 "army". Just to confuse things, records indicate that 1000 of the 1860 Army models (.44) were delivered to the Navy.
Re the most likely to be used by a particular Confederate Calvary unit (in your case the 17th VA), I cannot say. If I had to guess, I would say the 1860 Army which was produced in large numbers and was a very popular gun. There is also the question of issued vs battlefield pickup. If you are planning to join a reenactment unit or NSSA unit, you need to be certain as to what that unit uses/allows.