Let us know how it goes. The majority are very good shooters with ammo they like. Even wartime production guns seemed to have very good consistency.
Be advised, the "point blank" range with the rear sight all the way flat was I believe 547 yards, meaning aim at the middle of a standing enemy and it would hit him out to that range. What that means to the target or recreational shooter is that they usually shoot rather high at 100 yards. Some people make a new front sight blade so it can be zeroed at a closer distance. You can also stand up the sight and use either the notch or aperture sight on the standing leaf. I think one or the other (or both) can be set for 100 yards.
There was a thread on the forum I linked below about making a front sight blade for easier shooting at 100 yards. I thought it was a sticky at the top of the page for this section, but the one I was thinking of wasn't there. The thread about
accurizing the 1903 may have some of the sight info though, I didn't read it in detail. If its not in that thread, looking around should turn it up, it was a pretty simple way they were doing it.
http://www.surplusrifleforum.com/viewforum.php?f=36&sid=f113e2723bd0e66253a4cbbb3b84228d
ETA: Hey wait, look here. The topic of "how do I bring down my groupings?" is in the sticky section.
http://www.surplusrifleforum.com/viewforum.php?f=116&sid=f113e2723bd0e66253a4cbbb3b84228d
1903's having different stocks or other parts isn't unusual, they were rebuilt or repaired whenever needed. They were in general service quite a while, in reserve, and used by state Nat Guards for years after they went out of general service in the regular army. I personally think the other stock types besides the scant grip are more attractive. The early straight grips with finger grooves on the fore end and screw type cross bolts are nicest looking. Later straight grips did away with the finger grooves, and eventually used plain pins for the cross bolt reinforcement. The regular type pistol grip (as opposed to the scant, which was sort of a stop gap idea) stocks used for a while are very nice looking also. The details can get to be an obsession, or at least a matter of interesting study.
Another good reference for 1903 stuff,
http://m1903.com/