One thing I've been curious on, with some of the long range calibers or barrel burner wildcats, would it be worth having the barrel melonited or a similar process done to extend the life of the barrel?
338 Lapua? Really? Someone tell me why that's the best choice. Why would firing a 300gr pill be beneficial here? Plenty of short action calibers are still supersonic at 1k and with a good enough BC to make it count. If we were talking ELR or 1700+ that might be different. 6.5 would be my caliber for this. Creedmoor more specifically. Not because it's the best option, but I'd stand the best chance with it due to my data and load info available.
You realize .4 MOA at 1k is danged near world record, right? How about a more realistic goal? Like being able to calculate your dope for that shot in a year or even being able to land on a 2'x2' target out there.
If you are serious about this. It'd be a full time job and probably $50k of ammo, rifles, optics, reloading equipment, four wheeler, targets, flights to get hands on tutoring from "the masters", etc.
This is totally not the right forum to ask for advice on this type of thing. Try Snipershide. Grow some rhino skin before you post this over there.
Snipershide.com would have wanted the op hung for this post. Personally I don't thing it's a good place for the newbie. There are to many people who take a honest (even if impossible) question personally.
It's a wonderful place for after you get the basics.
While all the replies you may receive here are submitted with good intentions, the expertise needed will be more readily found on a "long range, precision shooting, sniper minded" type forum.
Hitting a 4" target at 1000 yards is far from unheard of. Hitting them consistently is another thing entirely. As stated up thread, calling and doping the wind is what separates the men from the boys and I'm nowhere near good enough to consistently hit a 4" target at 1000. I did hit a ground hog yesterday at 300 and my farthest hit to date with my .308 was at 1360 yards. It took 7 rounds, 58.5 minutes of elevation and eleven minutes of wind to get there but I finally hit it. Couldn't have done it here in IN, this was in VA.
Consistently hitting a MOA sized target (10") at 1000 yards is a reasonable long range goal to work toward. It will take lots of practice, but it won't take thousands of rounds to achieve.
Getting first-round hits on MOA sized targets from 500 out to 1000 is also a good objective.