Correct stock finish for M1903?

[WarPig1976]

There's an art to a hand rubbed oil finish. The last one on the bench took three months. I'm working on a oil finish on a Remington 700 stock now which may be ready in two because the grain in the walnut is tight.
All you need is time, time and a little more time.
BTW, you're not going to match decades of burnishing. Just stop when the wood doesn't take anymore, maybe 5 or 6 "coats". Wipe all the oil off or you'll have a sticky mess.