Rock on! I was deployed as an attachment to an Army SF unit back in 2006, after I left 3rd Recon. You guys are solid in my book. I believe it was 338th, maybe that sounds familiar? I'm not up to speed on all the Army units in USSO.
If it has a 20" round barrel and serial number less than 9,800 then it's the earliest version Winchester Model 63. Those are the rarest as only 9,800 were made.
If it has a 23" round barrel smooth receiver top and serial between 9,800 and 165,00 then you have a newer model. Yours appears to be...