The more the stamps, the less the value?

[ut1seabee]

The stock on your rifle is SC. The markings are not applicable if your rifle is a Remington.

[JOHN COOK]

All of the markings look to crisp to me.

john in SC

[King carp]

The reciever, barrel and small parts are remington marked. The bolt is not marked except for a dot on the handle.

[togor]

$500 is a great price. Good for you without it being outright larceny on the poor widow.

[King carp]

This rifle came out of a local gun shop that is closing up. I have known the owner for years and he was nice enough to give me a long time customer discount.

[Sunray]

"...the overall condition trump..." Does to most collectors. The stamps do tell the life/service story of that rifle though. They also mean the thing has been rebuilt by professionals vs some guy.
"...FJA is an original manufacturers stamping..." Inspector not the maker. Lt. Col. Frank J. Atwood to be specific. He only worked at Remington inspecting new rifles though.
Rummage around here. https://m1903.com/
FA 37 may be collector stuff. Depends mostly on the head stamp, but if it's still in the original boxes it'll have collector interest. The head stamp should tell you what variation of ammo it was. It is not .30 M2 though. It'll be either M1906 or .30 M1. No such thing as M2 in 1937. No non-corrosive primer ammo until 1952.

[Tom in N.J.]

To me, it looks like that stock was originally on a Smith- Carona M1903A3, large proof "P" is a dead give away. (along with the number in a diamond inspection mark ).

[King carp]

Thanks for the info. I guess the rifle is what is called a mix master. It is in great shape. I hope it is an accurate rifle. I look forward to trying it out
The ammo was not in original boxes. It came on stripper clips in a bandoleer.20190729_105237.jpg

[Merc]

There is one sure way to tell if it’s a Remington or Smith Corona stock. The spring groove end is square on Remington Stocks and rounded on Smith Corona stocks.

[King carp]

I take it this is from a Smith Corona stock?20190729_142140.jpg