Phew, tough one. While its got lets variation than a 1903, it does have all the same things you look for, but different aspects.
The best move (if time permits) is Ferris Book on the 1917.
Both rifles have the issue if shot with blanks for ceremonial purposes the throat is gone (uslay they have been shot for 30 years or more so lots of blanks)
Unfortunately the muzzle looks wonderful the the barrel sans a bore scope looks fine as well. The lob bullets sideways at 25 yards. The best tool is a Throat Erosion gauge, how much the bolt looks to have been cycle vs the rest of the condition is a clue.
Mixed parts versions are most predominant. People will build up an all matching parts gun and there is no telling if its artificial or not (toss up on the honesty of that)
Bad looking bores can be brought back to good looking with the right cleaning products.
They are easier to shoot as the peep is very good and the radius is very long.
They came in 3 mfg variations, Winchester, Remington and Eddystone . W the least built, Eddystone the most.
Original stocks will have the mfg letter on the front, though its very common to have been moved out of them.
A clean no mark stock other than the Eagle stamp is highly desirable.
Bad stocks are an issue as stocks are very expensive and no one makes aftermarket any more (Boyds did at one time) - a good stock will go in the $350 ragne.
Barrel dates and SNs can be as much as 3 months apart easily.
A different mfg barrel from the receiver usually means its been altered, there were not a lot of spare barrels made (until WWII)
WWII due to rifle shortage, they dusted them off, found a lot of bad barrels from storage corrosion and JA, RI and HS (I believe) made barrel for them. JA is a two grove standard right twist. RI and HS I think were 4. No dates on them.
They are good barrels. two grove shoots as good as the 4.
The original were 5 grove and left twist as that was the machinery from the Pattern 14 that proceeded it (303 for the Brits)
Cock on close action per SMLE , if it cocks on open its been altered (not a show stopper just not standard, there were conversion and still are)
Bolt is not smooth, its a nickle steel on bolt and the receiver. Kind of sticky. There are latter bolts all steel that I understand are better.
Head space is very generous, pretty much will close the bolt on a field reject gauge. Normal.
Do not try to use a head space gauge on them unless you know how to take the firing pin (striker assembly) out. The cock on close will crush the gauge.
They are solid guns, contra to the Urban Legends, Edsystones are not prone to cracking (all are if the right tools not used for taking the original barrel off regardless of who did it)
Most were re-arsenaled so have mixed parts and likely not the original finish (a variation on parkerized ). If its all blue black you got an untouched one.
Almost 100% of the parts have a id of mfg stamp on them (W, R, E). Some have numbers only, Ferris has a breakdown (400 numbers were Winchester)
None of the mfgs shared barrels, so if its got a non receiver mfg barrel on it, its been changed, they did not ship to anyone else to make up for shortages (of any parts). Ech mfgs was on their own. Remington and Eddystone were associated companies but totally separate production (and no where close location wise) and no sharing.
Winchester is a bit more valuable as it was the least produces (500k or so)
Remington next with 650k
Eddystone was a 1.4 or 1.6 million.
Condition trumps mfg.
Fun guns to shoot and accurate, easier on old eyes with the peep and I can sort of shoot them at 75 and 100 yards (my eyes don't work so good for iron sights)
Occasionally you will fine a P14 variation or parts (stock) with 1917 stuff mixed up and in.