Wow. Loaded questions.
Watch out for reclaimed drill gun receivers, there will be a weld near the cutoff switch. Any grinding marks or refinishing is a NO.
Don't accept commercial receivers with Santa Fe, or National Ordnance, or any other weird name. Smith Corona or Remington will be the only legit M1903A3 receivers.
Then it all comes down to original finish, correct arsenal manufacture of metal parts and furniture, and bore condition.
Provided there are no drill rifle or bubba issues, and the bore gauges well:
1. A refinished mix-master in poor finish or refinish is $300 to $450. Good finish $400 to $550
2. Reasonable matched receiver/barrel date, and correct stock with decent inspector cartouches, but mixed arsenal or refinished small parts in average condition $500 to $650. Good to excellent $600 to $750.
3. All correct arsenal parts and finish with matched receiver barrel date, non-sanded stock with sharp cartouches in average condition $700 to $850. Good to excellent $800 to the moon (I've seen all original and nice Remingtons and Smith Coronas go for $1,500-plus)
Here is an all correct Remington. I wouldn't let it go for any less than $1,000
Now, and all correct Smith Corona, probably a $1,200 gun
And I have a mix-master Remington parts gun which is probably a $400 to $500 gun. No pics
Hope all that helps