In 1,000 yard shooting, BC rules. A high BC bullet retains velocity better, giving it a shorter time of flight to the target, which gives the wind less time to act on the bullet.
The velocity most commonly seen with high BC bullets is 2950 fps, most chamberings used in 1,000 yard can hit this velocity and most are accurate around this velocity. This is due to barrel harmonics, most barrels have a sweet spot at 2950 fps. There is another node up around 3100 fps but not too many chamberings will reach that velocity without a large case volume for caliber or a very stiff load.
First starting out you may want to opt for one of the easier chamberings. The 6mm BR and it's variants (6mm Dasher, 6mm BRX) will all reach 1,000 yards with a high degree of accuracy, are not particularily difficult to load for, are relatively easy on barrels, have light recoil to make gun handling easier, and have been proven in competition. Best overall choice maybe not, best starting of choice maybe so.
The 6 X 47 Lapua wildcat (based on the 6.5 X 47 Lapua) may be another good choice, easier to hit target velocities, and some loads have proven to be very accurate.
The 6.5 X 284 is my personnal favorite, despite eating barrels at a rapid pace. I have found it easy to develop a good load (only took about 1/2 the life of the first barrel to hit on the ES/SD sweet spot ;D) and have only needed to test the load when changing barrels or lot numbers of powder. A few shots accross the chrono and done. I wish it had a little longer neck with the shoulder pushed back just a touch for a little less case capacity.
The straight .284 is making progress in competition, but I imagine the recoil of trying to hit 2950 fps with a 180 gr bullet makes gun handling a little more challenging in a light rifle. Haven't gone there yet, the 6.5 works so well for me I'm loathe to try something new.
I think all of the .30s work, and whichever one reaches 2950 (or the 3100 fps range) with at least a 90% case fill is a viable choice. I think the design of the .300 RSAUM has about the most ideal proprtions amiong the .30s with something in the 190 gr range. Now that Norma is making brass it would seem a good choice.
.338s? Well, I have a .338 RUM that when the barrel was fresh would print .3s with a 250 gr Lapua Scenar at 2950 fps. It was a chore to shoot in a lighter rifle, and made printing a small group very difficult from the rifle handling standpoint. And with a long string barrel heat is an issue, did one match with 20 round strings which made the barrel hot and me sore. I feel it has more than enough accuracy to compete though. The same would be true for the .338 Lapua. Maybe in a 40 lb rifle...
Anyhow.
Starting off you'll want to adhere to the KISS principle, a chambering that doesn't entail a lot of tinkering with brass and a lot of time in load developement so your time can be spent improving your skill set. The 6mm BR or the .300 RSAUM are probably the simplest choices, followed by the 6.5 X 284 (even with the limited barrel life) and straight .284.
With high quality brass you should be able to go with a no turn neck chamber, and if you talk to Dave Kiff up at PTG you can get a reamer to work with the dies of your choice. My reamer is dimensioned for a .297 neck and Redding dies. .297 might be a touch tight so I watch my case neck thickess. Buy the reamer, you will have to replace the barrel at some time and it makes duplicating the chamber a lot simpler.
Finally, regardless of what action, barrel and stock you choose, none of it will work properly without quality smithing, period dot the end. No matter the quality of the components, it won't work right with bad or even average smithing.
The result of the excellent smithing on my first full on custom rifle was I was wondering what was wrong because there was only one very small hole in the paper at 100 with the first four shoots out of the rifle and then holding over 1" to see if I was actually on paper, thought the scope broke or something.