+1 for what Promo noted.
Can't really go past an all matching serial numbered rifle. Also check hand guards for similar wear/aging to the main stock. Be aware though that if rifle went through the W R S then marking on the butt portion of the stock may have been scrubbed/sanded down. Also don't expect all parts on the rifle to be from the same manufacturer as in its almost 100 year life parts most likely would have been changed In service.
Good luck with your search. Never know what you might find. I've managed to find a P14 W MkI* (F) and a No.3 MkI* T (A) for under NZ$250 each recently. The No.3 MkI* T (A) is missing its mounts and scope unfortunately and it's sporting some crude aftermarket scope mounting holes on the side of the receiver, but hey they only made 421 of them!