Since you will be hand loading or buying expensive match ammo for this rifle (the milsurp '03 and Garand .30-06 ammo would be a waste in this new rifle) you might want to consider a calibre like .308 Win, since many of these types of rifles are already chambered for it.
This. The 1903 doesn't care, but M1s need a specific pressure curve range, or damage can result.
You can get one in .30-06, but it will be a custom proposition. You can get an off the shelf LR rig in .308 from a number of different places that will most likely suit your needs for 1/2 to 1/3 of the price.
That savings buys better glass, or a lot of practice ammo.