In the 1960's the M-14's and the M-16 that the Army issued me had O.D. green cotton web slings. This is what I was trained with and am familiar with, so this is what's on my M-1, M-1 Carbine, Model 1903A3, Springfield M1A. These slings were standard issue and are great for field use. The "combat sling" (civilians know it as the "hasty sling") is quick to assume from the standing position.
The leather sling is more for target range use, as noted above.
You do not need a reproduction, so many web slings were made during WWII that they are still plentiful. I buy my USGI surplus, unissued, still in original wrapper, web slings from Charleys Surplus for less that $10 each.
I have a "correct" reproduction cotton sling that I bought off eBay. There is a fellow on there that sells quite a few M1 parts. He is also an M1 armorer. His name is Thomas Smith and if I remember right, his screen name is SNOOK1969.