Re: Minimum caliber for between 1K and 1 mile?
for target shooting only, then you can thank a lot smaller than the 338. I would say either 30 cal or 7mm.
I shoot to beyond a mile (1,800 yards) very sucessfully here (as in the Las Vegas desert - 2,100 ft alt.) with a 7WSM running the Cauterucio 189s at roughly 2,950 fps. My brother does the same with his .284 winchester Improved with Berger 180s at 2,900 fps. If you are at sea level I'm not sure the 7mms will be supersonic when you get to 1,800 yards. But here at 2,100+ ft alt, they are virtually always supersonic at that range.
I have heard from some folks doing the shooting at the sniper rifle trials that the 300 Norma Magnum took the accuracy portion of the shooting category at 1,500 meters. I believe that the 300 Norma Mag running 208 AMax or 210 Bergers is a hell of a round. If I were not so focused on 7mm, that is one cartridge I would be looking at very hard.
If you are talking hunting, then the retained energy needs become critical. When hitting steel at distance, its not the primary concern - flat shooting, wind bucking becomes the primary issue.