Another m1903 with questions

Hello

I have a springfield armory m1903 that my father gave me and I'm just trying to figure out what I have because I'm selling my guns and don't know the price range on this one.

I'm hoping someone can help me decipher this one.

springfield armory m1903 serial #816271
has S A on the top end of the barrel with 12-32 stamped as well and the flaming bomb or whatever it is.

underneath the barrel on the very end of the wood it is stamped with RI

Then on the left side it has the inspectors stamp in the wood of SA with JFC under that and
outlined.

Can anyone tell me what all that means?

I don't want to overprice it but on the other hand I'd like to not give it away if I can help it.

Any help is appreciated.

Thank you.

Pics here would be invaluable. A picture heavy expose...