It took me years of searching to find an all military 03, then a bunch were released by the CMP, and now, they are gone. Don’t expect them to get any cheaper especially if it turns out those were the last bunch in till we get another Ronald Regan as President. At best that might be a couple of generations out there, I think it more likely the ice caps will melt first from Global Warming.
If I were looking for a 03 I would look for something with a good barrel. The WW2 barrels, particulary the High Standard, were good barrels. Every WW1 and 20's barrel I examined had been shot so much that the barrel was getting closer to a smooth bore than a rifled barrel. Sedgley barrels were good. Check the bedding, if the barrel is touching the top of the upper band, then you will have to rebed that rear lug or the action will stay bowed. I would check the slop in the rear sight, but it will be pointless. Only factory new or NM 03’s have rear sights that move easily without teeter tottering from side to side. I spent hours pounding and lapping my rear sight to take out all the left to right error.
I would replace the mainspring with the lightest Wolff mainspring. I think it is an 18 or 20 pounder. Original mainsprings are always worn out and a replacement spring tends to crispen the trigger pull. Also tends to increase it, but the lock time is a heck of a lot better.
If you can find the Marine Corp front sight put that in. It is wider and easier to see, brings the point of impact of the battle sight down to 200 yards. Also, given the choice between a pistol grip and a straight grip stock, all things being equal, get the pistol grip. The straight grip stock is positively painful to shoot; I can still remember the swollen cheeks and lips from the recoil. You will learn to point the right thumb straight ahead! Also, the pistol grip stock is a little longer, will keep your shooting glasses off the cocking piece during recoil.
I always shot the M1903A3's better than the 03's, at least out to 200 yards. Beyond that the fixed, and always off, quantum elevation of the A3 requires "Kentucky windage" to center the group.
Back in the 50's and 60's, civilian service rifle shooters generally shot with A3's. The military made it just about impossible to get a Garand, you could, if you traveled to Camp Perry, get a NM, but otherwise, all that were available were A3's. Of course that made it very difficult to earn your Distinguished, or get a President's patch. Shooting at 300 and 600 yards was a lot of work with a A3. Compared to the wonderful rear sight of a Garand the A3 sight is primitive. Windage on a A3 is irregular and then you have to hold off for elevation. The Club President did not get a Garand until the 80's, but, he was able to buy a Devine M1a in the 70's!. Till then, he was competing against National Guard, Reserve, AMU team members who had either matched out Garands or M14's while all he had was his A3.
Life can be unfair, and sometimes, it is planned that way.