picked up a 1903 need some advice

[yoopercollector]

In the OP the mag cutoff looks like something is wrong.

[Fred G.]

Yes, your rifle is a 1920 National Match 1903 that should have a bright polished bolt with either J5 under the safety lug on the bolt or a J6 on top of the bolt handle base. The J5 or J6 bolt should be one of those bright bolts with the swept back handle.
I own rifle 1181006, barrel date 11-19 which has a bright J5 bolt with a swept handle.
Your rifle was originally bought and owned by an officer in the military. They were the only persons allowed to purchase or own one of these rifles until 1921.
The muzzle on the barrel would not have a Star Gauge stamp on the crown.
Your magazine cut off would quite possibly have the serif letters on it because at that time, Springfield Armory was only making Mark I cut offs (with block letters) and Rock Island Arsenal was a source of none Mark I cut offs for the 1920 National Match rifles. My rifle however does have a cut off with block letters and color case hardening.
Some of these rifles were prepared for and mounted with Lyman sights, like yours. Your rifle has a correct rear sight without the top notch on the ladder and has the correct adjustment knobs on it and the correct serrated trigger and serrated butt plate and is complete except the bolt was originally a National Match bolt with J5 or J6 stamping with a bright polish and a swept back handle. Your stock is correct with the correct inspectors stamp on the left wrist. Hand guards at that time on 1920 NM rifles were both concave (high Hump) like on yours and straight like on my rifle. A Wonderful rifle.
Do Not drill or tap anything on it or change anything except for the bolt which should be a J5 or J6 NM polished bolt and have a safety with Block letters.

[Promo]

Fred said it - but to add, your inletting is for the Lyman 48 rear sight. The deep cutout suggests that it probably was for the rarer long slide Lyman 48, but this would require you to check if it fits.

A very nice rifle and should make an easy restoration! And valueable also! If you ever decide to part with it, send me a PM!

[Herschel]

The correct Lyman 48 sight for the 1903 NM and 1903 NRA sporter had a sight slide numbered to 125. In the era of these rifles the elevtion scale numbered to 150 was called the long slide. Some 1903 rifles that were used in long range competition had long slide sights but nearly all had the regular slide. (elevation scale numbered to 125).

[m1903rifle]

Looks like a straight bolt handle. If so, not correct for 1920.